There are many types of reamer. Machine, taper, hand, adjustable, etc. Each has a specific use. For the purpose of discussion, I'll use the machine reamer as an example:
A machine reamer has three main purposes:
1) To size a hole
Drills do not make an accurate hole. A two-fluted drill will tend to drill an equilateral tri-lobed hole, especially until the margins are engaged in the work. A lightly fed drill of sufficient length will drill a helical tri-lobed hole with a helix angle equal to the helix angle of the drill. Due to this effect, along with the additive effect of drill point runout, and the "orbiting" effect that naturally occurs when the web is not perfectly ground, an oversize hole is produced. The severity of the effect depends on feed, speed, material, drill grind, lubricant / coolant, etc. There are standard tables for predicting the amount of oversize by drill size.
A reamer, properly used, can improve hole size accuracy by 10 to 15 fold over a drill and is much more repeatable.
2) To improve the holes cylindricity. (there's that word again)
This goes back to the tri-lobed hole. A reamer is a hybrid metal displacing and metal cutting tool with many more flutes than a drill, negating the lobing effect that occurs with a two-flute tool. As a consequence, running a reamer in a drilled hole will improve the cylindricity of the hole simply due to it's cutting edge geometry.
3) To improve the surface finish.
Drilled holes normally have a rough surface finish. This can be unnacceptable in precision fits, bearing locations, etc. Like a drill, a reamer is a hybrid cutting and cold-flowing tool. Unlike a drill, the cold-flowing quality is used to improve the surface finish of the hole. To make this possible, a reamer has two cutting edges:
The first cutting edge is the relieved chamfer of the margin at the "business end' of the reamer. This edge performs the initial hole sizing operation and has sufficient edge relief to permit light cutting. However, it is not relieved as much as a drill, causing some light springback to occur.
The second cutting edge is the margin, which runs the full length of the flutes. This edge has little to no relief, making it a poor cutting edge. Thus, when the material springs back against the margin, it burnishes or "cold flows" the material as it's unrelieved cutting edge "wipes" over the surface. This operation dramatically increases the surface finish of the hole.
Good surface finishes are the key to precise fits and long-lasting bearing surfaces.
All other reamers are a hybrid of these general principles. Taper reamers have a more relieved margin, to permit making a taper from a step-drilled hole. Adjustable reamers are just that - adjustable for size. Adjustable "blade-type" hand reamers are useful if you need to enlarge a hole slightly. A two-flute drill is a poor choice for enlarging a hole slightly as it will tend to grab. Hand reamers operate on the same principle as machine reamers, except they generally have a greater chamfer angle for easy cutting and include a pilot to help locate the reamer in the drilled hole.