You have three basic concerns when thinking about changing tire width
- Will different tires fit your rims?
- If fitting wider tires, will they clear the frame and fork (and leave enough clearance for mud or debris if riding off road)
- How will different width tires affect the ride and handling of the bike.
There are various resources for determining tire width / rim inner width compatibility, including the chart on the Sheldon Brown page linked to in other answers here. Tire manufacturers should provide min and max rim widths for each tire model and size.
Whether you can, or want to drop to a 2.1" from a 2.8" tire in terms of ride and handling depends on what type of bike you have and what riding you are doing. Presumably at 2.8" you have an MTB so you need to think about the potential for reduced bump absorption and traction with narrower tires.