The owner typically controls the object, and in many cases, objects can control each other if they share the same owner, although several flags modify this behavior (e.g. Inherit/Trust, Mistrust, and Wizard).
Games may limit the number of objects a player may own by instituting quota limits.
Other things to own
There are other niche forms of ownership as well. All MUSH servers assign an owner to each attribute on an object, which may be different than the owner of the object. This was once useful, but has become much less so.
PennMUSH associates an owner with each lock on an object and allows multiple owners of a @malias. TinyMUSH and TinyMUX support a single @malias owner which typically must be a wizard in order for the @malias to be used by everyone.