Learn Hardcore Icelandic: Það er búið að hita teið.

Here það is a dummy subject (an “it/there” that doesn’t refer to anything concrete), similar to English it is done or it has been done. Icelandic often uses það to build impersonal sentences where no real subject is named:

Það er búið að ... = it is finished to ... So það doesn’t mean a specific “that” here; it’s mainly structural.

What is the function of búið in Það er búið að hita teið?

Búið is the past participle of búa (in this construction), used in the idiom að vera búinn/búin/búið að + infinitive, meaning to have finished doing / to be done (with) doing. So the structure is:

er (present of vera, “is”)
búið (past participle, “finished/done”)
að hita (infinitive phrase, “to heat”) Together: It is finished to heat the tea → idiomatically: The tea has been heated / Someone has heated the tea (already).

Why is it búið (neuter) and not búinn or búin?

Because the participle agrees with the grammatical subject. Here the subject is dummy það, which is neuter singular, so you get búið. If you use a real person as the subject, it changes:

Ég er búinn að hita teið. (male speaker)
Ég er búin að hita teið. (female speaker)
Ég er búið að ... is generally only for neuter things/children, and is uncommon for adults.