Mi promesis al mia amikino, ke mi helpos ŝin prepari manĝon morgaŭ.

Because -is is the Esperanto ending for the past tense.

So:

• promesi = to promise
• promesas = promise / am promising
• promesis = promised
• promesos = will promise

In Mi promesis..., the speaker is talking about a promise made earlier.

Because Esperanto uses the preposition al for the indirect object, meaning to.

So:

• Mi promesis al mia amikino = I promised to my female friend

This works like English to my friend. Esperanto usually does not mark this idea just by word order; it uses al clearly.

Amikino means female friend.

It comes from:

• amiko = friend
• -in- = female suffix
• amikino = female friend

So the sentence specifically says the friend is female. If the friend’s sex were unspecified or male, you might see amiko instead.