Quote acceptance is the moment the customer agrees to your quote as it stands: the work described, the price, and the terms in the note. Until then, the quote is an offer you have made. Once it is accepted, both sides have agreed to something, and the deposit, the start date and the payment terms in the quote take effect. Acceptance has to match the offer. A reply that says yes but changes the price, the scope or the terms is not an acceptance; it is a counter-offer, and it is your turn to agree to it or not.
Acceptance should leave a record. A yes on the phone is real but leaves nothing to point at. A text saying "go ahead" is better, though it rarely says to which version. A signature on the quote, an email reply quoting it, or a button press that is logged against that exact quote are better again. Whether a particular acceptance forms a binding contract depends on your terms and the law in your state, so for large jobs, take advice on what your terms should say.
In practice
A roofer quotes $8,900 to replace a tiled roof with metal sheeting. The owner replies: yes, if you can do it for $8,500 and include new gutters. That is a counter-offer. The roofer can decline it, accept it, or send a revised quote for $9,600 that includes the gutters at $700. The owner accepts the revised quote, and that one becomes the record. The first quote is simply an offer that was never taken up.
Partial acceptance works the same way. If a customer wants three of the five items on your quote, the clean answer is a new quote with those three, so the accepted document matches the job you will do.
In Quote Desk
The customer accepts by pressing Accept this quote on the link, and the quote's page records the date. Acceptance is for the whole quote as sent; for some lines and not others, they decline and you send a new quote with the lines they want. The accept link page explains what is recorded.