An upward force is any force that counteracts the force of gravity. Buoyancy is an example of an upward force because it pushes an object away from the Earth's center of mass.
Force is any sort of push or pull interaction for an object. Forces tend to make objects change direction, change motion or stay in motion. One of the forces that affects every single object on Earth is the force of gravity. Gravity pulls all objects to the center of Earth's mass, which is why objects will sit on the surface of the Earth and not move or lift into the air unless another force is applied to them.
Gravity can be thought of as a "downward force" because it pushes and keeps everything down onto the ground. For this reason, any force that goes in the opposite direction of gravity, such as buoyancy, is an "upward force." In fact, every object that is sitting on the surface of the Earth is not only experiencing gravity, but it is always experiencing an upward force as well.
For instance, a book sitting on a table stays on the table due to gravity. However, the table is also equally pushing up on the book in a reactive force, which keeps the book sitting on the table. If there were no upward force on the book, the book would fall right through the table.