It might be easier to understand the bulkiness of a group with some kind of model set. But as espen said, it literally refers to the size of the group.
Examples of non-bulky groups would be the cyanide (-CN) and azide (-N3) ions, which are small, linear, and shaped like "bullets." The classic "bulky" group is t-butyl, -C(CH3)3. All those methyl groups create quite a bit of steric hindrance.