Predicate is Сказуемое.Roles of words in a sentence are: subject, predicate, object, attributive etc.
Well, normally predicate is a second most important member of a sentence or a clause. Usually it is a verb.
"I go home." I - subject, go - predicate.
Participle:
Я убит. I am killed. Убит is a predicate therefore it is in a short form.
Убитый человек лежал на земле. Here predicate is лежал. Убитый is an attributive of человек and it is in a long form.
Adjective
Виноград зелен. The grape is green. Short form.
Я не люблю зеленый виноград. I don't like green grape. Long form