One of my favorites is the "no-gore" option. No longer do I need to watch pixelated bunnies get decapitated as I'm running around the game. It also seems to stop the game from lagging when hordes of zombies are attacking during a blood-moon.
The second, and maybe most important, new addition is being able to connect multiplayer through Steam. No more will I need to dig around computers and write down IP addresses every time my kids want to play the game together. That is a major hassle averted.
On top of those, the backgrounds are nicer, the underground caverns seem more natural in their formation, and there are TONS of new things to build and items to collect. In particular, I have received banners for defeating monsters in quantities of 50. These banners make it easier to defend the home from said monsters later. I also have enjoyed the new yo-yo weapon. It's a little ridiculous, but effective nonetheless.
Terraria is an inexpensive game that provides a huge return in terms of enjoyment. It truly is fun for the whole family.