A nozzle/injector/gigleur is a small threaded part or a insert which is used to restrict the flow of water towards the brewing group of the espresso machine. A nozzle can be found in a variety of shapes and sizes, but they all have a small hole.
In most cases a nozzle is made from machined brass, but you will also find them from Stainless steel, for instance with Marzocco. And they are threaded into the brewing group. A good example are the E61 style of brewing groups, which have the nozzle in the top.
Most nozzles range from a diameter of 0,5mm all the way up to 1,0mm. This does depend on how much water you want to come true the brewing group.