it arrives with hardmode
No world starts with the Hallow outside a handful of secret seeds. It appears the moment the Wall of Flesh dies, as a diagonal band cut from the surface all the way to the bottom of the world, converting everything eligible along the way. That band can land on existing Corruption or Crimson and overwrite it. It can also land on your base. The first thing worth doing after killing the Wall is walking the line to see where it fell, rather than assuming your town survived.
what it can and cannot convert
The Hallow takes stone, sand, ice and dirt carrying grass. It cannot move through mud, which makes the Jungle and glowing mushroom biomes effectively immune, although the initial Hardmode band still converts any plain stone sitting inside them. Sunflowers stop its surface creep exactly the way they stop the evil biomes. Hallow and evil cannot share ground, and each one blocks the other.
That last point is usable. Seeding Hallow along the border of a Corruption or Crimson biome walls the evil in without a Clentaminator, which matters before the Steampunker shows up. The cost is that you have traded one spreading biome for another, and the Hallow will take the rest of the world just as cheerfully.
the tile math
An artificial Hallow needs only 125 blocks, the lowest requirement of any biome in the game, counting Hallowed grass, Pearlstone Block, Pearlsand and Pink Ice Block. The counter is a tug of war: each Hallowed tile adds one and takes one off both evil totals, and each infected tile does the reverse. A room built at exactly 125 falls out of biome the instant one Crimson block creeps into range, so overshoot by a comfortable margin.
You can build a Hallow before Hardmode with seeds or Blue Solution carried in from another world. It gives you the background, the water color and the music, but no Hallow enemies spawn there. Lightning bugs still turn up at night, which is the one odd exception to that.
what is worth farming there
The Underground Hallow beneath it is the real payoff. Soul of Light drops there and nowhere else, and Crystal Shards grow back on exposed pearlstone indefinitely, so one cleared corridor becomes a renewable supply you can walk every few in game days. Anything killed in the Hallow can drop a Hallowed Key for the Dungeon's Hallowed Chest and the Rainbow Rod inside it, and fishing the biome produces the Crystal Serpent.
The enemies do not play the way the scenery looks. Unicorns charge fast and hit for a lot, Pixies swarm in numbers, and Gastropods snipe from off screen. Early Hardmode Hallow will end an unprepared run faster than the Corruption will.
keeping track of it
The Dryad reports the exact percentage of Hallow and of evil in your world when you talk to her. That readout is the only honest measure of whether your trenches are holding, and it is worth checking every so often through early Hardmode instead of waiting until something visible goes wrong. She treats the Hallow as good and the evil as bad, but she will not call a world pure until all three are gone. Beating Plantera once halves the spread rate of every one of them.
name and origins
To hallow something is to make it holy, so the name reads as holy ground. Unlike the Corruption, it has no alternate version: a candy themed counterpart was sketched out early in development and dropped before release. A few secret seeds hand you one from the start, including Celebration Mk 10, which grows Hallowed grass on Floating Islands at world generation and lets you build a Hallow biome long before Hardmode.