Learn Russian: Вам будет очень уютно: номер отлично оборудован. - You will be very cozy: the room is excellently equipped.

Оборудован is a short-form past passive participle from the verb оборудовать (to equip). It acts just like a short-form adjective to show the result of an action. Because it describes номер, which is a masculine noun, it takes the masculine zero-ending. It simply means the room "is equipped".

Why do we use the dative вам instead of the nominative вы?

The first part of the sentence is an impersonal construction expressing a physical or emotional state. In Russian, the person experiencing a state like being warm, cold, or cozy (уютно) goes into the dative case. It literally means "To you it will be very cozy."

Why is будет needed before уютно?

Because уютно is an adverb describing a state, it cannot show time on its own. To express that this state happens in the future ("will be cozy"), we must add будет (it will be). Impersonal sentences like this always use the third-person singular form for the future tense.

Doesn't номер usually mean "number"?

Yes, but it is also the standard Russian word for a hotel room. Because the sentence describes a space being cozy and excellently equipped, it definitely means a hotel room here. If you were talking about a room in a normal house or apartment, you would use the word комната.