Indirect object + verb + subject. Not your usual sentence structure, but in the case of piacere (to please, to like) that's the way it works in Italian, and here's why: In English, you say that A likes B. In Italian, though, the same meaning is understood in different terms: B pleases A. Here are some examples:
Agli italiani piace il calcio. (Italians like soccer. Literally: Soccer is pleasing to Italians.)
Ai professori piace insegnare. (Professors like teaching. Literally: Teaching is pleasing to professors.)
Mi piacciono le carote. (I like carrots. Literally: Carrots are pleasing to me.)
Note that in these examples, piacere is conjugated to match the subject of the sentence; in the first example, agli italiani piace il calcio, piacere is conjugated in the third person singular form, to match with calcio (soccer) and not with agli italiani (all Italians). Other verbs that follow this construction of inversion and behave similarly to piacere are listed below.
VERBS THAT ACT LIKE PIACERE
bastare
to be sufficient, to suffice
dispiacere
to displease, to upset
mancare
to be lacking, to miss
occorrere
to require, to need
servire
to serve, to be of use