You can find more on choosing motors and gears at the Choosing a Motor and Gearing Combination page.
"Gear motor" refers to a combination of a motor plus a reduction geartrain. These are often conveniently packaged together in one unit. The gear reduction (gear train) reduces the speed of the motor, with a corresponding increase in torque. Gear ratios range from just a few (e.g. 3) to huge (e.g. 500). A small ratio can be accomplished with a single gear pair, while a large ratio requires a series of gear reduction steps and thus more gears. There are a lot of different kinds of gear reduction.
In the case of a small transmission ratio N, the unit may be backdrivable, meaning you can turn the output shaft, perhaps by hand, at angular velocity w and cause the motor to rotate at angular velocity Nw. A larger transmission ratio N may make the unit non-backdrivable. Each has advantages for different circumstances. Backdrivability depends not just on N, but on many other factors.
For large N, often the maximum output torque is limited by the strength of the final gears, rather than by N times the motor's torque.