Explanation:

1 : a place in which public records or historical materials (such as documents) are preserved an archive of historical manuscripts a film archive also : the material preserved —often used in plural reading through the archives.
2 : a repository or collection especially of information. archive. verb. archived; archiving.
Archive is a file which has been compressed to reduce the size of the file.So in effect, archiving lets you tidy up your inbox by moving messages from your inbox into your All Mail label, so you don't have to delete anything. It's like moving something into a filing cabinet for safekeeping, rather than putting it in the trash can.
Example : .ZIP