It means the sprite must fit within that box, but it can be smaller (or rather, it should probably be that size, but unused pixels can be transparent).
Animates sprites are just sequences of different sprites displayed over time, so all the individual frames must fit the rules, but things can change between frames (such as position, palette, etc). This can mean that the entire animation as seen by the player can appear to be larger than the sprite size limit, although each frame is still within the limits.
In practice, a character can actually consist of multiple hardware sprites, and thus appear larger. For example, the NES used 8x8 hardware sprites, but most characters on the system were larger - this was done by building each character out of multiple sprites. These sprites didn't even have to be arranged in a grid, they could overlap, and clever designers used this to seemingly break the NES's limitations, such as by giving Mega Man more colours than is normally allowed:
(Source:
http://www.dustmop.io/blog/2015/06/08/nes-graphics-part-2/ )
Note how the face overlaps some of the other sprites' boundaries, and how the overall shape of the sprite isn't a rectangle.
On most modern platforms, this hardware sprite trickery no longer happens, because modern hardware deals with vector planes and textures, "sprites" are just flat planes with a texture on them, and the size limitations are very large (and constrained by RAM and VRAM rather than by pixel size). When people give a sprite size limit in the context of these platforms, it's more of a stylistic thing, it tells the artist what the maximum size should be.
