Hypertrophy is an increase in the size of cells in your body. In the fitness world, when we talk about hypertrophy, we're talking about muscle hypertrophy, or getting bigger muscles.
Your muscles are made of myofibrils: long rods of muscle tissue, which themselves are made of little units called sarcomeres. When myofibrils increase in size, this is known as myofibrillar hypertrophy, or functional hypertrophy.
These muscle fibres are surrounded by cells containing a liquid known as sarcoplasm. When these cells swell, commonly due to increase in muscle glycogen, this is known as sarcoplasmic hypertrophy, or non-functional hypertrophy.
If you're looking to get stronger, the preferred type of hypertrophy is myofibrillar. This is best achieved by working out with very heavy weights and doing sets of only a few reps. Very low numbers of reps with heavy weights also improves neural efficiency, meaning your muscles become more effective and therefore stronger.
Low reps and heavy weight is the fastest way to get stronger, but not the fastest way to get ripped. You should also be very careful when lifting or pulling heavy weights as the chance of injury is higher.
If you want your muscles to get bigger, you should be aiming for sarcoplasmic hypertrophy. You can do this by doing sets of 10-15 reps with moderate weights. This is the quickest and most effective way of growing muscles, but it is not the best way to get stronger.
If you do your exercises between these ranges, roughly 5-10 reps of heavy weights, you can strike a balance between myofibrillar and sarcoplasmic hypertrophy, meaning you'll get stronger and bigger.
It's important to be aware that hypertrophy will only occur if you also eat enough protein and rest properly between workouts. For growth and strength gains to continue over time, you also need to progressively increase the weights you workout with.