A romp ride with a group of friends
This factor and the enemy types/bosses lead to a formula that revolves heavily around combat (whereas in Minecraft, it's more about building/mining). Your focus isn't so much about getting that ore, but about getting the ore to make better armor and equipment. This was obviously intended in giving you the satisfaction of getting 'buffer' in universe.
Playing with friends is addicting and fantastic, as you get stronger, dig together into the depths of the earth, increase health/mana, find a variety of items that improve stats such as regeneration, knockback, etc., reach a wide variety of biomes/environments, and tackle intimidating bosses. It also helps that, akin to Mikecraft, Terraria is almost constantly being updated. These are not games that just sit in the rut; new ideas are being pumped in constantly.
Overall, Terraria is just so much fun with a group of devoted buddies. I feel like you'd be missing out if you were only playing the single player, because there are no "Omg guys! You will not believe what I found in this chest!". But then again, even in that case it's still entertaining. And multiplayer is always easy to pull off because you can transfer all your items between worlds. And the game isn't all that expensive!