You would say this to a family member or a significant other (spouse, boyfriend/girlfriend, etc.). You can use the verb нравиться (Мне нравится она = I like her, as an example) if you're talking about a friend where romantic feelings aren't appropriate but you want to show that you think positively about someone.
@irenearlet - If you mean why you would write "ona" in "mne nravitsya ona", it's because the verb is reflexive. "She" (ona) is the one actually performing the action, even though the subject is most likely "I" (in dative case, mne). The literal English translation would be something like "she is liked to me".