What are the benefits of venturing into the Nether?

The Nether is the only way to acquire Glowstone, one of the brightest light sources available along with the Jack O' Lantern, and an ingredient in the creation of the only redstone-toggleable light source. It is also the only way to acquire various brewing ingredients, to wit, Netherwart, Ghast Tears, and Blaze Rods. Netharrack, the material the Nether is built out of, will burn indefinitely, unlike wood. Zombie Pigmen, found only in the Nether, are an unlimited source of Gold Nuggets, which can be combined into Gold Ingots. It is also a near-unlimited source of lava.

Apart from the more general fact that there are resources there that you can't get anywhere else, up until recently, you also needed to visit the nether in order to get stuff required for you to reach the ender dragon, considered to be the final boss. Nowdays you can buy the critical components from villagers, so the trip is no longer strictly required.

As Per the Minecraft wiki:

• The nether can used for traveling traveling large distances on the above ground map quickly
• The nether contains block types not seen anywhere else such as:
  • Nether Wart (For Potions, can only be grown in the nether)
  • Netherrack
  • Soul Sand
  • Glowstone Blocks (Alternative to Torches)
  • Nether Brick
  • Nether Brick Fence
  • Nether Brick Stairs
  • Blaze Rods (Used in creating potions and Alchemly lab)
  • Magma Cream (Used in creating potions)
  • Ghast Tears (Used in creating potions)

There are five mobs in the Nether can only be found in the Nether:

• Ghast
• Magma Cube's
• Blazes (Only in Nether Fortresses)
• Zombie Pigmen (though these can spawn in the overworld when lighting hits a pig)
• Wither Skeletons (Also only in Nether Fortresses)

The Nether is also the only place to find Nether Fortresses which contain Nether Bricks and Blaze Spawners. Also the Nether has no night/day cycle and no weather. The only sources of natural light come from the lava, fire, and glowstone located there. Also a compass is useless in the Nether as it will just spin continuously in random directions and the same goes for the night/day cycle clock that can be crafted.

For more detailed information I would recommend reading the whole Minecraft Wiki Nether Page.