A drogue parachute is a parachute

Parachute

A parachute is a device used to slow the motion of an object through an atmosphere by creating drag, or in the case of ram-air parachutes, aerodynamic lift. Parachutes are usually made out of light, strong cloth, originally silk, now most commonly nylon...

 designed to be deployed from a rapidly moving object in order to slow the object, or to provide control and stability, or as a pilot parachute to deploy a larger parachute. It was invented by Giovanni Agusta in 1911.
A drogue parachute is more elongated and has a far smaller area than a conventional parachute, and thus provides less drag

Drag (physics)

In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

. This means that a drogue parachute cannot slow an object as much as a conventional parachute, but it can be deployed at speeds at which conventional parachutes would be torn apart.

The drogue parachute's simpler design allows for easier deployment.