Just to add to pacificamatt's correction, there are two cases where you can use the word rather.

(1) Using it as an emphasis to the degree of something. For example:

"That knife is rather sharp."  OR "It's rather hot in here."

Here you're using the word rather to emphasize that the knife is very sharp. I guess you could say that it another way of saying very.

(2) When comparing two things you can use the word rather to indicate the one you prefer.

"You want to take the bus to school, I'd rather walk." OR "I want to walk rather than take the bus."

pacificamatt does a good job of going into depth with your example, I'm just trying to show in general which situations you can use the word rather.

"I'd rather" means "I prefer."

In the context of the Maroon 5 song, he's singing about cuts ("so much deeper than they seem"). The person he is singing to wants to cover these cuts up (bandage them). He wants to "let them be" (meaning do nothing with them, leave them alone).