When you put quotes around something, it becomes a string. Strings are common objects in essentially every programming language.
Mathematica has a function called ToString to make things into strings. You can use Map to map ToString onto a list:
Map[ToString,{1,2,3,4,5}]
Note: Strings often appear in output with their quotes hidden, so if you want to see them, you'll have to run InputForm on the output to see that the quotes are there.
