A counteroffer is one possible response to an offer. It is (1) an offer from the offeree to the offeror (2) about the same subject matter, but (3) it proposes a different terms. See Restatement (Second) Contracts ยง 39(1).
Suppose, for example, that Brian offers to purchase Brianna's condo for $399,000. Brianna responds with this offer: "Thank you for your offer. I will sell you the condo for $451,500."
Brianna's offer is a counteroffer.