An isolation exercise is one where the movement is restricted to one joint and one muscle group. For example, the leg extension is an isolation exercise for the quadriceps.
Specialized types of equipment are used to ensure that other muscle groups are only minimally involved - they just help the individual maintain a stable posture - and movement occurs only around the knee joint. Most isolation exercises involve machines rather than dumbbells and barbells (free weights), though free weights can be used when combined with special positions and joint bracing.
Those who seek to improve the look of their body without necessarily maximising their strength gains (including bodybuilders) would put more of an emphasis on isolation exercises. Bodybuilders use isolation exercises mostly to achieve better muscle definition, when they already have enough muscle mass. An isolation exercise may be used in advanced routines to pre-exhaust the target muscle before performing a compound exercise, or to additionally stress the target muscle after performing a compound exercise.