Freeware refers to software that is, well, free of cost to use for an unlimited period of time. The opposite of freeware is referred to as, appropriately enough, payware.
Freeware may be proprietary in nature, in that the source code may be closed to users, but not necessarily.
It should be noted that freeware may not, in all its uses, be free. Depending on the license used by the author, it could be that a piece of software qualifies as freeware for personal, non-commercial use, but for commercial use, it becomes payware.
Thus, software that advertises “free trial runs” and the like does not count as freeware. It also does not include software that is not fully functional without components that must be purchased. Both of these refer to shareware.
Pirated software is also not included in this definition, as it is made to be free and costless against the will of the license holder.