Recently my civic has had a slight hesitation of the starter when first turning the key on an occasional basis. Yesterday turned the key and nothing, it didn't turn over. Plenty of electricity. 1 hour later it cranked fine. The next day I stopped at a store came back out and again nothing. But turned it off tried again and a normal start. Previously I had tried multiple starts.
You almost certainly have a Starter Motor problem. A small possibility is that you have a bad connection somewhere such as at the connection terminals on the Starter itself or possibly the Terminals on the Car Battery. A loose or badly corroded Battery terminal would normally cause other problems though such as a poor charging ability and therefore you would see a dead battery but this problem can be intermittent. Try having someone stand in front of your car. Turn on your Headlights. Turn your key as if to start your car. If nothing happens and your headlight dim a lot then you likely have a weak battery or a possible short somewhere. I am a DIY guy not a Mechanic but I would try this before I bought a new Starter as they cost "BIG" bucks for a Honda. Depending on the age of your Civic I would probably head to the Scrapyard for a replacement starter. Recycle/Reuse and most of all save a paycheck.