1. To suggest or propose doing something on behalf of someone or for someone's benefit. Jim offered to cook dinner because I wasn't feeling very well. She offered to speak to the boss to clear the issue up.

2. To suggest or propose giving to someone as a gift, favor, payment, compensation, etc. In this usage, a noun or pronoun is used between "offer" and "to." He offered $500 to me so that I wouldn't speak about the incident to the police or the media. I'm offering half my assets to my partner in exchange for full control over the intellectual property.