To offer means to present something to someone for them to accept or refuse. When you offer your friend half of your sandwich, you're giving them the choice to take it. When a store offers a sale, it's making products available at lower prices. When you offer to help your neighbor carry groceries, you're volunteering your time and effort.

The word captures that moment of reaching out with something: an object, an opportunity, or your own help. A teacher might offer extra credit. A company might offer someone a job. Your mom might offer you a ride to school. In each case, the other person can say yes or no.

An offer (as a noun) is the thing being presented. “I'll give you five dollars for that book” is an offer to buy it. When someone makes you an offer you can't refuse, they're presenting something so tempting that almost no one would want to turn it down.

Notice that offering involves some generosity or willingness: you're putting something forward without forcing it. That's different from demanding, commanding, or insisting. When you offer something, you're leaving the choice in someone else's hands.