Biggoron's Sword is the largest, mightiest weapon available to use in the N64 game the Legend of Zelda: Ocarina of Time. It is only available as Adult Link. It can be assigned to your usual sword button B.
The main plus point of Biggoron's Sword is that it does twice the damage of the regular Master Sword. It can take down most incidental enemies - keese, Deku baba, tektites - in one hit. Failing that, a jumping attack (Z-target your enemy and press A) with Biggoron's Sword will do twice the damage again. This technique makes fighting an Iron Knuckle a considerably less stressful experience. However, it takes two hands to wield this thing, so while holding it your will not be able to utilise your shield, but they're useless against Iron Knuckles anyway... It will also drastically reduce the length of boss battles, increase the range (and therefore damaging potential) of your spin attack, and makes playing tennis against Phantom Ganon or Ganondorf slightly easier.
It was originally created by a big Goron blacksmith called Biggoron, and then came into the ownership of the head carpenter at Gerudo Valley, who broke it. That's where you first pick it up, while broken. You then fix it by taking it from him and back to Biggoron. After that it can be used as adult Link whenever you like.
Getting hold of the sword is not necessary to complete the game. You can do that just by using the Master Sword. However, I think it's definitely worth putting in the effort to get Biggoron's Sword. And the ludicrously protracted trading sequence that you need to go through in order to get it is fun in its own right, even if it is just an extended side-quest. Throughout this sequence a small red and yellow flashing arrow on your map screen will indicate where in the map you need to go for the next part of the trading sequence.
How to get Biggoron's Sword
You need to be adult Link for this whole sequence. You will also need access to Epona before you can do it, because there are two timed deliveries which need making, both of which take too long to be made on foot (or by warping). To save time on one of these deliveries, it's worthwhile to purchase a Magic Bean as Young Link and plant it in the soft dirt near the entrance to Dodongo's Cavern on Death Mountain: this forms a useful shortcut when you come back as adult Link. You may also find it useful to have the Hookshot on hand to cross the bridge at Gerudo Valley. The Song of the Sun is also pretty handy for a little time-warping here and there, but very much optional.
- Kakariko Village: go and find the girl who asked you as a child to catch all of her Cuccos for her. She will give you a Pocket Egg. Use the Sun Song or just wait a few days, and eventually it will hatch into a Cucco. Cuccos love waking things up. Find Talon, the moustachioed co-owner of Lon Lon Ranch, asleep in one of the houses in Kakariko Village. Take out the Cucco in front of him and it will crow, waking him up. The Cucco is now happy: take it back to the girl and she'll swap it for a special blue Cucco called Cojiro.
- Lost Woods: Cojiro wants to cheer somebody up, and the ideal person is in the Lost Woods. Head left from the first room and you'll find the girl's brother sitting grumpily against a tree stump. Take out Cojiro in front of him and he'll swap it for an odorous, suspicious-looking Mushroom to take to the Potion Shop in Kakariko Village.
- Kakariko Village again: head into the Potion Shop and talk to the old hag. Give her the Mushroom and she will quickly turn it into a super-strong Potion to give to her son (!) in the Lost Woods again.
- Lost Woods again: the bloke who was sitting against the tree stump seems to have vanished, replaced by a young Kokiri girl, who explains that the boy has been turned into a Stalfos. No matter: show her the Potion and she will demand it be returned to her, and swap it for the Poacher's Saw which the boy presumably left behind.
- Gerudo Valley: if you haven't completed the Gerudo Fortress section yet (which is likely, if you're aiming to get Biggoron's Sword relatively early on in the game), the bridge to the Gerudo Valley will be broken down. You can cross this by riding at it full tilt on Epona, or by using your Hookshot. Just beyond the bridge you'll find a small group of carpenters near a tent. The Poacher's Saw is the property of the head carpenter - give it to him and he will give you a Broken Goron Sword.
- Death Mountain: climb all the way to the top of Death Mountain and head to the right of the entrance to the crater, where the biggest Goron you've ever seen will unfold himself to say hello. This guy - Biggoron - is a Goron blacksmith and he'd be happy to repair the sword for you, except he's got sore eyes. He'll give you a Prescription to take to King Zora.
- Zora's Domain: show the Prescription to King Zora and he'll give you an extremely perishable Eyeball Frog, whose eyeballs are the active ingredient in the eye drops that Biggoron requires. Unfortunately, taking it out of the icebox means you only have three minutes to take the Eyeball Frog to the professor by Lake Hylia, before it goes bad. Warping is no good here. Leave the Domain at high speed and leap down the Zora River to Hyrule Field, then call Epona and ride across the field towards the lake. Always keep one carrot in reserve while riding Epona - use them all up and she takes an age to recover them all, meaning your journey will be slower. Leap both fences outside the lake entrance and ride up to the laboratory...
- Lake Hylia: the time limit is pretty stiff but with luck you can get here with more than a few seconds to spare. Quickly show the Eyeball Frog to the professor and he will process it into some of the World's Finest Eye Drops. You now have four minutes in which to return these to Biggoron. You'll have to leave Epona at the bottom of the ramp up to Kakariko Village, and run the rest of the way. Remember, rolling is slightly faster than running - hit A repeatedly while you ascend Death Mountain to go faster. Use the magic plant as a shortcut if possible.
- Death Mountain again: Quickly show Biggoron the World's Finest Eye Drops and he will be very happy, and begin to mend the sword. He'll give you a Claim Check to give him later. If you can't be bothered to wait, you can use the Sun Song to make three or four days rapidly go by, then give Biggoron the Claim Check to receive Biggoron's Sword!
Biggoron's Sword is essentially an upgrade of the Giant's Knife referred to below. The Giant's Knife has the same properties as Biggoron's Sword, except that it costs a fortune, and will break after only 100 slashes.
Sources: my own hazy memory, ign.com, issue 25 of N64 Magazine