Assent means agreement. If you nod your head in assent, you agree to something or you assent to it.
As a verb, assent is generally followed by a phrase beginning with the word "to:" You assent to a plan, an agreement, or to an idea. Assent is also something that you can give. You can give your assent to marry your partner if he or she asks really nicely. The opposite of assent is dissent –– which means disagreeing, or even protesting in a formal way.