The most important dimension is the internal rack width. EIA standard 19 inch racks are common in IT, while 23 and 24 inch racks are used by telecommunications service providers.
The external width is also important. Wider cabinets obviously take up more floor space. They also provide more internal space for cabling. PDUs (Power Distribution Units) can be mounted at the side of the rack if there is not enough space. This takes up zero rack space (0U height).
There is no single internal depth standard, even for 19 inch racks. It can be 600mm, 800mm, 900mm, 1000mm, 1100mm or even 1200mm.
Rack and server heights are measured in "U" units. Popular cabinet heights are 15U/24U/42U and 47U extra-tall.