Say, if someone uses the password 'gwpmkq' and a site uses plain MD5, they store cc733aac12981561dfc4944dd34a595f in their database. Now, even a stupid attacker can google for a hash search engine, input the hash and get the password in seconds.
On the other hand, with salting the value to be hashed could be something like 'firstname.lastname@example.org:@362#^h6329hgtew:gwpmkq'. That won't be precomputed anywhere.
Of course it's also a good idea to either try to keep the salt secret or use a per-user random salt (which you store in the database). But when someone gets a full database dump, chances are they'll also get the salt.