Learn Russian: Мне очень нравится эта украшенная комната.

It comes from the perfective verb украсить (to decorate). For verbs ending in -ить, we drop the -ить and add the past passive participle suffix -енн-. Notice there is also a consonant mutation here: the с in the stem changes to ш, giving us the base украшенн-. Finally, we add the adjective ending -ая.

Why does украшенная have the ending -ая instead of the short ending -а?

Because it is a full-form participle placed directly before the noun it modifies, so it acts exactly like an adjective. It must agree with комната in gender, case, and number. Since комната is feminine, singular, and in the nominative case, the participle takes the standard feminine nominative ending -ая. You would use the short form украшена if you were making a statement like 'The room is decorated' (Комната украшена).

Why is the room (эта украшенная комната) in the nominative case if it is the thing I am liking?

This is a great reminder of how the verb нравиться works. It literally means 'to be pleasing to'. The sentence is structured as 'This decorated room is very pleasing to me.' Therefore, the room is the grammatical subject (doing the pleasing) and stays in the nominative case, while the person experiencing the feeling is the indirect object in the dative case (Мне).