Single-joint exercises (isolation exercises) are those in which only one joint moves throughout the entire range of motion and therefore one muscle or muscle group is worked to a great extent.
Examples of single-joint exercises are bicep curls, leg extensions, leg curls, lateral raises, etc.
Multi-joint exercises (compound exercises) utilize more than one joint and work multiple muscle groups simultaneously.
Examples of multi-joint exercises are squats, bench presses, overhead presses, deadlifts, lunges, etc.
Should I be doing single-joint exercises or multi-joint exercises?
The short answer: For most people who are looking to drop a few pounds, get stronger and overall more healthy - multi-joint exercises should make-up the majority of your program.
Here are a few reasons why:
1) Burn more calories. By working more than one muscle group, you burn substantially more calories than doing any other single-joint exercise.
Also, not only will you burn more calories in a single session, but performing heavier compound exercises boosts your metabolism for 24-48 hours after your workout. This means you are burning more calories for up to two days after you finished!
2) Strength gain. During multi-joint exercises a large number of muscle fibers work at once, so you’ll be able to lift heavier weights. More weight lifted translates into faster strength gains, especially when you’re a beginner starting a new workout routine.
3) Move Better. Working the body with mostly multi-joint exercises takes the body through natural movement patterns and teaches the body how to move better. Squatting, pressing, rowing, and deadlifting, all teach the body coordination and how to fire multiple muscle groups simultaneously.
Also, when perfoming single-joint exercises, most people tend to work their favorite muscles more than other muscles which can lead to muscular imbalances. This can affect the body's natural movement patterns and increases the risk of injury.
All this isn't to say you should never do a single-joint exercise. Isolation exercises can complement compound (multi-joint) exercises. However, I strongly suggest that multi-joint exercises make up a bulk of your exercise program.