In English the person who "likes" is the Subject. THe person/object "liked" is the Object.
in Russian the person/object which is "liked" is the Subject. And the "liking" person is a complement in dative.
Я нравлюсь Маше! Masha likes me! Literally: I am-pleasant(appealing) to(for)-Masha
Я ей нравлюсь! She likes me!
Мне нравится читать тексты Сурен
(Suren is a Mongol woman here, whose Russian is more pleasant than that of 99% of educated Russians. It could be great if she wrote a book:) But for a book one needs some ideas).
Note the difference in word order.
Despite technically, "мне" is not a Subject, just a complement ("to me"), we feel it is natural to put it first when we speaking about ourselves.
So if in "Маше нравится Вася" and "Вася нравится Маше" both orders are more or less neutral... when we speak about "me", the _neutral_ word order is:
Я нравлюсь Маше.
Мне нравится мороженое.
Other orders would change meaning:
"мороженое мне нравится" - speaking about ice-cream, I like it. What I don't like is having hot ttea and cold ice-cream simulataneously.
"мороженое нравится мне" - It is I who loves ice-cream! Not Vasya.
"мне мороженое нравится" - [here meaning depends on intonation]
This difference is because when we speak about Masha and Vasya, it might be story about either one of them.. or likely both. When I speak about myself - it is in most cases the story about myself:)