Learn Icelandic: Það er bjart í dag.

Það means "it". Just like in English when we say "it is bright", Icelandic uses það as a dummy subject for weather and general conditions where there isn't a specific person or thing doing the action.

Why is the word for bright spelled bjart instead of the dictionary form bjartur?

Adjectives in Icelandic change to match the gender of the word they describe. Because the dummy subject það is grammatically neuter, the adjective takes its neuter form bjart instead of the masculine bjartur.

Is er the same verb used for people?

Yes, er is the "is" form of the verb vera (to be). It is exactly the same word you use when saying "he is" (hann er) or "she is" (hún er).

How does í dag translate to "today"?

It literally translates to "in day". Icelandic uses the preposition í meaning "in", together with dag meaning "day", to create the set phrase í dag, which is the standard way to say "today".