We call it the pump. Scientists call it hyperaemia or cell swelling. Aside from being an incredible feeling, the pump also has significant muscle-building benefits. A hydrated cell stimulates protein synthesis and inhibits protein breakdown. Chasing the pump also icreases satellite cell activity and the muscle cell's ability to continue expanding.
Just using a muscle will lead to an increase in localized blood flow, but there are specific training practices that best lend themselves to inducing a skin-splitting pump.
Tension and Tempo
The formula for generating hyperaemia is simple yet effective. As part of your training, use lighter loads, higher reps, and tempos that increase time under tension.
Load up an EZ bar with your 12-15 rep max for curls. Do 10-12 reps with this tempo: lower for three seconds, then take three seconds to lift it back up. Avoid lowering fully into the stretch position and flex hard for a second in the contracted position. Your biceps will be blown up and flooded with blood.
Lower body example: Set up on a lying leg curl machine and use a weight you can get 15 reps with. Do 10-12 reps without lowering the weight all the way in order to maintain tension through your hamstrings. Take 4 seconds to lower, a brief pause near the bottom, and 2-3 seconds to raise it back up.
Prepare to be humbled and taken aback by the obscene amount of blood flow to your hamstrings. Yes, you'll be doing fewer reps than you could using the same weight, but going slowly and keeping the muscle under tension instead of letting it go at the top or bottom of the lift will make you hurt.
Training in this manner doesn't just increase blood flow to the muscles you're working, it also creates a powerful occlusion effect.
The Occlusion Effect
Occlusion is when you decrease the available oxygen to the target muscle(s). If you've ever seen someone wrap a band around a leg or arm while lifting, that's what they're doing.
But you can do this without putting your limbs in tourniquets, which is handy when you're training a body part that doesn't lend itself to being wrapped (chest, back, shoulders). By manipulating the tempo and range of motion in a given exercise, you can create a similar effect.
Start your chest work with a dumbbell press at a low incline. To create an occlusion effect in your chest and drive a lot of blood into the area, try the following tempo, form, and ROM prescription.
Take 3-4 seconds to lower the weight until your elbows are just below parallel. Pause for 1-2 seconds. Then take 3 seconds to press the weight up. As you press up, rotate your hands so that you finish in a semi-supinated (palms facing each other) position. Stop two inches or so short of lockout. Stopping here will force you to maintain the tension in your chest, creating the occlusion effect.