Glass fusing is the process of using a kiln to join together pieces of glass. If you apply heat to glass, it will soften. If you continue to apply heat, the glass will become more fluid and flow together. Two or more pieces of glass will stick (or "fuse") to each other. When the right kind of glass is heated and then cooled properly, the resulting fused glass piece will be solid and unbroken.
Many people also use the word "fusing" to include bending and shaping glass using the heat of a kiln. This manipulation can take many forms, but the most common is slumping, where a mold is used to cause already fused glass to take on the shape of a bowl, a plate, or similar object. Other kinds of manipulation done with fusing techniques are combing, which involves using a tool to distort the shape of the glass while it is hot, and fire polishing, which uses a kiln to heat the glass just enough to make it shiny and smooth.
Another category of kiln-forming activity involves the use of molds to form glass into more complex shapes. Virtually any shape that can be formed in clay or wax can also be made in glass. These more advanced kiln forming processes include kiln casting (melting glass into a mold inside a kiln, pate de verre (forming shapes by heating a "paste of glass" inside the kiln), and glass casting (pouring molten glass into a mold). These processes tend to be more complicated than basic fusing and slumping.