I was looking for the name of the class of verbs that 'gustar' belongs to and I found it in the Big Red Book. Gustar is a 'reverse construction verb'.
http://www.espanol-ingles.com.mx/spanish-grammar/reverse_constructions.shtml
In the case of 'gustar', what appears to be the direct object (the thing being liked) is the subject of the sentence for conjugation purposes.
So, if I want to say "I like tennis", tennis is the subject for conjugation purposes so we say "me gusta tenis". The more equivalent sentence in English is "tennis is pleasing to me".
If I want to say "She likes flowers", flowers are the subject for conjugation purposes so we say "le gustan las flores". The more equivalent sentence is "the flowers are pleasing to her".
Note that in both cases, we effectively converted a sentence that uses the "active voice" into one that uses the "passive voice".
The thing that makes it hard for us English speakers is this notion that the subject of the sentence follows the verb. Likewise, the notion that direct and indirect pronouns appear before the verb is also a strange concept to us English speakers.
Reverse Construction verbs - gustar

Robert-C7
December 1, 2014