Photography lighting is an umbrella term that involves not only the process of lighting an image but also the tools that are involved in the process.
Of course, when we speak about photography lighting we refer to both natural and artificial lighting. For the sake of clarity, we shall stick to artificial lighting only.
There are many kinds of artificial lighting in photography. They are divided mainly into strobes and continuous lights. Strobes are further divided into the smaller speedlights and the larger strobes. Apart from these, there is a world of light modifiers such as softboxes, diffusers, reflectors, strip boxes, foam cores, snoots grids and so on.
Basically, these tools are meant to shape the light and make it conducive to shoot in specific situations. They also help in setting the mood of the images. The term also involves the process of building the lighting of a scene.