Circular needles are two short needles joined together by some sort of cord. So where you normally use two needles in this case your two needles are joined to each other. They can be made out of a lot of different materials and the cords vary a little. Very old one had like a wire cable thing and some are a nylon material and they have some now that are very flexible and I don't know what they are made of.
You use them for different reasons. You can use them to work in a circle, forming a tube. You can use them to make hats (tube around head), sweaters (tube around body), or socks (tube around leg and foot). When you use circulars in this way you can avoid seaming. You have to have a circular of the appropriate length. Hats you usually do on 16 inch circulars but when you eliminate enough stitches for the top of the hat, so that the stitches no longer reach around the 16" needle you have to compensate by going to double pointed needles (which can be used for tiny tubes and are usually used for socks too), or to two circulars. Two circulars can enable you to make tiny tubes, just like double pointed needles do. You can use two circulars to make socks. So, you use circulars (one or two) to make any kind of thing you go around and round on.
Another use for them is to hold a lot of stitches. 14" are about the longest straight needles and they only hold so many stitches, but circulars come in many lengths (16, 24, 29, 36 and even longer, are some). So if you are making an afghan with 360 stitches you may need a circular to hold all the stitches. You can still use the circular to do flat work, you just treat the needle tips as you would straights and exchange them in your hands at the end of each row.
Many of us like circulars over straights for all our knitting. I use them a lot, although I only use the 10 straight needles, which I don't mind for something small like a scarf, or even a baby sweater sometimes. But circulars have their advantages, you can't lose a needle so easily (if it is in use at least), you can move the stitches away from the end of the needles and dont's have to worry about stitches falling off the ends when you are resting a project. Heavy weights are taken off your arms and laid in your lap. With two of them you can make just about anything. So many people love circulars.
They are not hard to use. You can even learn on them, or take them us as soon as you want.