A "pump" is when the muscle you are exercising becomes larger than when it is at rest. This is caused by the body shuttling more blood to the working muscle than normal to help quickly deliver key nutrients, mainly oxygen.
This process can be enhanced with specific ingredients that support nitric oxide "NO" production, alongside being properly hydrated.
As the body delivers these nutrients to the muscle at an increased rate, it allows the muscle to perform better/longer, thus resulting in a better workout experience.
While the pump has an amazing aesthetic appeal, the enhanced blood flow to the working muscles has downstream benefits in delivering important post-workout nutrients. Always remember to follow up your workouts with a serving of protein!