Two-dimensional repeating patterns
Like one-dimensional repeating patterns, two-dimensional repeating patterns always have more than one possible unit of repeat. There are usually one or two obvious possibilities, but there are often many others that are less obvious. The only requirement is that the whole object (apart possibly from its edges) can be made by repeating the unit.
The tiles in the image below themselves form a unit of repeat, since all the tiles are identical (apart from minor variations). However, the tiles around the edge usually have to be cut to fit the actual floor.
The red square shows a possible unit of repeat. This unit is of particular interest, because the pattern in it is identical to the pattern on each tile.
This tartan is a two-dimensional repeating pattern.
Two possible units of repeat are the squares outlined by the dotted lines below.
Explore these ideas further in Tessellations.