This word always reminds me of that line from Pirates of the Caribbean: “I’m disinclined to acquiesce your request.” Acquiesce is a fancy, French-derived word that simply means to agree.
More specifically, though, it means to agree passively, to “submit or comply silently or without protest”. That’s because, according to the Online Etymology Dictionary, it comes from Latin “acquiescere ‘remain at rest,’ thus ‘be satisfied with,’ from ad- ‘to’ + quiescere ‘to become quiet’”.
So, acquiesce is more than just a fancy word for “agree”; it’s a specific word used to describe quiet agreement. If you haven’t expressed disagreement, you’ve acquiesced.