The most standard crank design is the three piece design, also known as "square taper". In this design, the three parts are the (1)left crank, (2) the right crank/chainring, and (3)the bottom bracket spindle. The spindle usually had a square taper, and the crank is press fitted onto this taper. However, there were several other sub-designs where instead of square taper, the axle had a splined shaft. Shimano called their splined shaft "Octalink". There was also ISIS, but it is rare now.
In this design, the axle and one side are a combined piece. The second piece is the other crank arm, which is attached via 2 pinch bolts. Usually 24mm. The Shimano name is HollowTech. This design allows the crank bearings to be outside the shell, thus you will sometimes see "outboard" in the specs rather than Hollow. The two are synonymous.
The number of pieces can be derived from the Technology. SquareTaper and Octalink are always three piece cranks, whereas Hollowtech II is always two piece.