What is the point of using archive.php instead of index.php?

index.php and archive.php might be the same but don’t have to be the same. index.php will display your blog post archive and in the absence of archive.php (or other more specific archive files) it will display your date, author, etc. archives as well. But it doesn’t have to.

You can, if you want, display your archived differently that your main blog index. That is the point of those specialized files– they allow you to alter the look of specific pages without having to write complicated conditionals into the index.php file.

The difference between the two files is what you make of it. That difference can be a lot or none.

Reference

http://codex.wordpress.org/Template_Hierarchy