Round nose pliers are an essential jewellery-making tool. If you are just starting out in jewellery making and are wondering what tools to buy, then round nose pliers would be very close to the top of my list. You will want to use them every time you make a loop on a head pin or eye pin. I use mine for opening and closing jump rings and split rings. You will need them if you want to create coils of wire. You can also use them for making wire wraps and I confess I have even used mine to grip a needle and pull it through a tight bead (although this does risk breaking the bead!).
Round nose pliers, as the name suggests, are recognisable from the round shape to the nose of the tool. This is what makes them so good for creating wire wraps and loops: you simply need to bend the wire or wrap it around the nose of the pliers. If you look closely at the photo, you should see that the nose is narrower near the tip. So, depending where on the pliers you wrap your wire, you can create larger or smaller loops.
When I am making split rings, then you can wrap the wire around a wider point of the teeth. If you are making a set of rings, then it is a good idea to mark the position you use for your first ring on the round nose pliers. Then you can wrap all your loops around this same point and you will end up with a consistent sized set of rings.
There are many different brands of pliers on the market. I recommend that you avoid the very cheapest brands as they tend not to be terribly robust. You do not necessarily need to spend a fortune though, particularly if you are just starting out and not sure whether this will become a long-term hobby. However, if you do end up making a lot of jewellery, you will be glad you made the investment.