What it is
An answering service picks up calls your business cannot get to and captures who rang and why. That is the whole idea. What varies is who or what does the answering, how much they know about your business, and what they can resolve without you.
How the call actually reaches them
You keep your number and divert unanswered calls, usually after about twenty seconds of ringing. Your customers dial the same number they always have and never see anything different.
What a good one captures
A name, a contactable number, what they actually wanted, and how urgent it is. A better one also answers the question if it can, so the caller gets what they rang for instead of waiting for a call back.
How to tell if you need one
Look at your mobile call log for the last fortnight and count the unanswered incoming calls. Halve it, to be conservative. Multiply by the share that would realistically have become work, and then by what a job is worth to you. If that number is bigger than a few hundred dollars a month, the phone is costing you more than covering it would.
When you do not need one
If you answer nearly every call, or your enquiries mostly arrive by email or form, this is not your bottleneck and you should spend the money elsewhere. Anyone who tells you otherwise is selling.