After Jaime loses his right hand, he wonders "is that all I was? A swordhand?"; his maiming presents him with a severe identity crisis: he has always thought of himself as "the Warrior" and nothing more, and now suddenly, he cannot physically be that person any more. His initial reaction to the obliteration of his identity is to will himself to die, until Brienne asks if he is so craven that he's willing to give up, implying that she sees that there is more to him than his notorious reputation, that there is a man there who exists apart from his swordhand.
After Jaime and Brienne return to King's Landing, Tywin Lannister urges his son to break his Kingsguard vows, and even gives him one of the two Valyrian steel swords reforged from Ned Stark's great sword Ice. Jaime, who once would have given his right hand for such a sword, has no use for it now, and sees it as a bribe from Tywin - so instead, he turns around and gives the sword, which he names Oathkeeper, to Brienne of Tarth. Along with the sword, he gives Brienne a quest to find Sansa Stark, and in doing so, to find Jaime's own lost honor. That last part of the quest, Jaime's honor, which becomes the foremost thing in Brienne's mind in A Feast for Crows, is a sign that in some important ways, Jaime, in many important ways, actually is the sword he gives to Brienne.
First of all, the conflation of men and their swords (their literal
ones, not as metaphors for their penises!) happens quite a lot in the series: there are
“sworn swords” aplenty, and “sellswords” where the identity of the
(almost always) men is subsumed in their weapons (in contrast, we never
hear of “sworn bows” or “sellbows” or “sworn axes” and “sellaxes”,
right?). Then there is the Kingsguard, the institution which so shapes
Jaime: The Kingsguard lose their family names and emblems, lose the
ability to continue their names (when they swear to hold no lands, take
no wives, father no children), when they become the King’s Sworn Swords,
and they are called the "White Swords" who
live in the White Sword Tower. And then there’s Arthur Dayne, the idol
of Jaime’s youth, was nicknamed “the Sword of the Morning.” So
men=swords quite a lot!
And what does that mean for Jaime? Jaime was a sworn sword who broke
his vows, a White Sword who used a golden sword to kill his King. Like
Ned Stark’s sword Ice, Jaime is broken and remade twice, tempered twice
by fire. The first time the fires are metaphorical: Jaime, the Young
Lion, Aerys’s sworn sword, became the Kingslayer because of Aerys’s
wildfire. The second time they are literal: Jaime’s sword hand is gone,
and flames cauterize his wound (not to mention the boiling wine with
which Qyburn cleanses the corruption from it). Both fire AND water are necessary to forge a sword, and so Jaime’s
confession to Brienne comes when they are both immersed in water, as
Jaime burns with fever. How’s that for symbolism?
Like Jaime, Ned Stark’s sword ice is broken down, and remade, and it comes out of the forge completely different, made into two swords,
Widow’s Wail and Oathkeeper, neither of which resembles the original
Ice’s smoky grey. Instead, these new swords are, oddly enough, Targaryen
colors: blood red and black (“waves of night and blood upon some steely
shore”). Tobho Mott tells Tywin and Tyrion that the swords chose their
own colors, no matter how hard he tried to make them Lannister crimson,
part of the magic of Valyrian steel (which can also kill White Walkers,
let’s not forget!)
Then there are the names and appearances of the swords. Jaime/Brienne fans talk about Oathkeeper a lot but
Widow’s Wail is also important, I think. It is a smaller sword, made
for Joffrey, who is a boy. Both Oathkeeper and Widow’s Wail have lion’s
head pommels, but Widow’s Wail, Tywin Lannister’s wedding gift to
Joffrey, screams out LANNISTER. Its hilt is more ornate than that of
Oathkeeper, “the arms of its cross-guard done as lions’ paws with ruby
claws unsheathed” and Joffrey uses it to destroy learning/reason,
represented by the book that Tyrion gives him as his wedding gift.
Moreover, Widow’s Wail has one of the really standard types of sword
names. Almost all the named Valyrian steel swords we know either reflect
something about the house they belong to: the Starks had Ice, of
course, because “Winter is Coming”; the Lannisters had (now lost)
Brightroar; the Mormonts Longclaw; the Targaryens had (lost) Blackfyre.
The other naming convention seems to be a sort of boastful commentary on
the sword’s function: the Tarlys have Heartsbane; Visenya Targaryen
wielded Dark Sister, and we also know of Red Rain, Nightfall and Lady
Forlorn. Widow’s Wail, of course fits in with this second group
perfectly. Significantly, this sword which is a visible symbol of
Lannister power and pride, is given successively to the tangible proof
of Jaime’s love for Cersei, his two sons by her, who are, though Tywin
doesn’t know it, purely Lannisters: Joffrey, who is utterly unworthy of
the sword and who uses it once for an utterly unworthy purpose, and
Tommen, who is far too young to wield it.
And then there is Oathkeeper, which, along with one other sword
(Arthur Dayne’s Dawn, which may or may not be Valyrian steel and which
has a distinctive color like Oathkeeper - “pale as milkglass”) has a
name that is neither a threat (like Heartsbane or Widow’s Wail) nor a
link to a specific House. And look who names it: Jaime Lannister, the
most notorious oathbreaker in Westeros. Now, many clever people have
argued that he names the sword after Brienne, and though I like the idea
of it, I … think it is actually named as an act of aspiration for himself.
Oathkeeper is a gift from Tywin Lannister to Jaime, a promise of
greater gifts to come if Jaime will do what Tywin wants, and wiggle out
of his Kingsugard oaths, resume his rightful position as the head of
House Lannister, and be “the man you were always meant to be.” But Jaime
rejects all of what Tywin offers him: he names this amazing sword Oathkeeper,
a rebuke to his father who would have him break his oaths (AGAIN!) and
he rejects everything Tywin offers him, his “place” as the head of House
Lannister, his inheritance of Casterly Rock. In turn, Tywin tells Jaime "you are not my son." Those are cruel words, but they also free Jaime from the burden of being the Kingslayer, Cersei's lover, Tywin's son, the expectations of his family. That freedom will not fully come to fruition until A Dance with Dragons, when Jaime abandons the Lannister army he is leading back to King's Landing and disappears with Brienne to who knows where for who knows what purpose, although we may surmise that it may be to face Lady Stoneheart's judgment for being a Lannister (Lady Stoneheart, who is busy hanging anyone who's a Frey or a Lannister, or who fought for them, using the principle of collective guilt by association, even though obviously we know that not every Frey or Lannister foot soldier planned the Red Wedding.)
So these two swords, Oathkeeper and Widow’s Wail, are, for me, the
two parts of Jaime, who is broken and changed: Widow’s Wail is the Jaime
that was, the boastful warrior who made made many widows wail, the
sword that is practically a giant blinking neon sign of Lannisterness,
given to Jaime’s children by Cersei, which is used to destroy something
fragile and precious (a rare book) as Jaime destroyed Bran’s life;
Oathkeeper is the Jaime that he now wants to be, from the name
to the fact that he gives it away to the only true knight he knows to
the fact that he wants it to be used for something that is benign (as benign as a sword can be), which is to protect Ned Stark’s daughter with Ned Stark’s steel.
And Oathkeeper, wielded by Brienne, ties into the idea that the sword representing Justice: Ice was last used to cut off the head of the
innocent Ned Stark (and before that seen when Ned was executing a
Night’s Watch deserter whose crime was to be terrified of nightmares
come to life. I know, I know, rules are rules, blahblahblah, but
Gared-in-the-books/Will-on-the-show hadn’t committed any actual crime
and in fact had delivered a warning that no one cared to hear).
Oathkeeper, in contrast, is used by Brienne to deliver justice to the
remnants of the Brave Companions for their many crimes, and to protect
and defend the children at the Inn of the Crossroads.
Jaime tells Brienne that Sansa Stark is his last chance for honor and
gives Brienne the sword that is his best self, the self he wants to be
(Goldenhand the Just, instead of the Kingslayer) and names it Oathkeeper, which Brienne uses for justice, not to kill the innocent, he is, in a way, delivering himself to Brienne's safekeeping.