Learn Hardcore Icelandic: Hún fer í bankann til að tala við stjóra um launin. - She goes to the bank to talk with the boss about the salary.

í + accusative is used for motion into a place: í bankann = into/to the bank (going there).
í + dative is used for location: í bankanum = in/inside the bank (already there).
til + genitive means to/towards, often used with people or places you go to without the idea of entering (e.g., til læknis “to the doctor”). With buildings you physically go into, Icelandic normally uses í, so say í bankann.

What does the -ann ending in bankann mean?

It’s the suffixed definite article in the accusative singular for a masculine noun. The noun is banki (a bank). With the definite article:

Nominative: bankinn (the bank)
Accusative: bankann (to/into the bank)
Dative: bankanum (in/at the bank)
Genitive: bankans (of the bank)

Can I say í banka instead of í bankann?

Yes. Í banka = “to a bank” (nonspecific). Í bankann = “to the bank” (a specific or understood bank). In everyday speech, Icelandic often uses the definite form for routine destinations (í bankann, í búðina, í skólann) even if English would say “to the bank/the store/the school” generically.

Why is it til að tala rather than just að tala?