Wat is een watersnijmachine?

How do waterjets work?

Take ordinary tap water and pressurize it to 60,000 psi (4,000 bar) and force it through a very small hole. Mix the water with garnet abrasive and you have a very thin stream of water traveling very fast that will rapidly erode most materials. 
Some waterjets are "pure waterjets" and don't add the garnet abrasive. These are used to cut softer materials, such as food, rubber, and foam.  

What can waterjets cut? What can't they cut?

Waterjets can cut just about any material that can be made into a sheet and placed in front of them. 
The most popular materials are metals (especially aluminum, because it's relatively soft and cuts quickly), because waterjets can cut intricate shapes to a high precision quickly and economically. Since metals are the most common material cut by machining shops, waterjets tend to cut a lot of metal.
Waterjets also commonly cut stone and glass, because the waterjet can get intricate shapes not possible using traditional machining methods. These materials are popular with artists who like to work with these materials and waterjets because it lets them create almost anything they can envision.
Among the very few materials that waterjets cannot cut are diamonds and tempered glass. Diamonds are too hard to cut (and there may be a few other very hard materials that can't be cut). Tempered glass will shatter when it is cut with a waterjet (tempered glass is designed to shatter when it's disturbed and is frequently used in windshields for this very reason). 
A few advanced ceramics are so hard that it's not economical to cut them. Some composite materials (layers of different materials sandwiched together) can't be cut because the water can seep between the layers and "delaminate" the material. Many composite materials cut just fine, though, and there are some techniques to cutting laminated materials.