There are several requirements that must be met for there to be a binding contractual agreement between two parties. One of the requirements is that one party must offer to do something in exchange for something that the other party agrees to do (the "consideration"). That other party must then accept that offer to create a binding contract. So, for example, a person selling a house offers to sell it for a certain price (the consideration) and somebody may accept that offer by agreeing to pay the purchase price or some other negotiated amount, thus creating a binding contract (subject to any cancellation terms in the purchase agreement).
All of that's nice and clean when the contract at issue is something as formal as a purchase agreement for a house or car. But we potentially form binding contracts, especially verbal or oral contracts, more frequently than just the examples of buying a car or house, which don't happen very often for most people. Things can become a little messier absent a formal written agreement. The issue whether there was even a binding contract then sometimes arises.
Sometimes those arguments occur over whether there was actually a legally enforceable offer for the other party to accept. But I want to talk about the back end of a potential deal, acceptance of the offer. Parties trying to avoid contractual obligations will sometimes argue, among other things, that they never accepted the offer; therefore, there is no binding contract for a court to enforce. That then implicates the legal requirements for what is necessary to constitute a party's acceptance of a contractual offer.
The overarching legal principle is that acceptance of an offer is a manifestation of assent to its terms made by the party considering the offer in a manner invited or required by the offer. So if the agreement requires a signature to be accepted and binding, then only a signature counts as acceptance and creates contractual obligations. Written contracts can also require that valid, binding acceptance requires the acceptance to be delivered to a certain place (like a corporate office) or in a certain manner (like first class mail).
On the other hand, although a party making an offer may specify how it shall be accepted, failing that anything that amounts to a manifestation of the determination to accept the offer is sufficient, including an oral response. Manifestation may be partly by written or spoken words or by other acts or failure to act. The conduct of a party is not effective as a manifestation of assent unless the party intends to engage in the conduct and knows or has reason to know that the other party may infer from the conduct that it's intended as a manifestation of assent.
This may come up in your personal life most frequently when you hire a contractor for anything around your house. The contractor will usually review your situation and prepare a bid, quote, or estimate for the work. You then decide whether you want the contractor to do the work for the quoted price. If you do, then you may do nothing more than tell the contractor that you want the work to begin. You may not actually sign anything, and you certainly don't execute contractual instruments as complicated and formal as you would when buying a house or vehicle. But that doesn't mean that your obligation to the contractor is any less enforceable.