approve
To officially agree to something or think it is good.
To approve means to officially agree to something or to think favorably of it. When your teacher approves your science project topic, she's giving you permission to move forward with it. When parents approve of their child's new friend, they think that friend is a good influence.
The word carries two related meanings. In the first sense, someone with authority gives formal permission: a principal might approve a field trip, or Congress might approve a new law. In the second sense, someone forms a positive opinion: you might approve of how your friend stood up to a bully, meaning you think they did the right thing.
The opposite is disapprove, which means to think unfavorably of something or to refuse permission. If you hear that something has been given approval, it has received official permission or acceptance. Notice that approving doesn't always mean you're excited about something. A parent might approve of vegetables for dinner without jumping for joy. Approval can mean accepting something as good enough or acceptable, even if it's not your favorite choice.