A pump and filter are often referred to as the equipment, since they are required for any pool. A pool must be equipped with a pump and a filter. Really though, that is not well-stated; to be accurate, a pool must be equipped with a PROPERLY-SIZED pump and a PROPERLY-SIZED filter. Yes, that’s better.
While pool chemicals are often given sole credit for maintaining optimal water clarity, the reality is that proper circulation (via the pump) and filtration (via the filter) greatly – greatly – assist your pool chemicals with water clarity. The overall process of circulation and filtration is more effective and efficient when the pump and filter are properly-sized, given your pool specifications (mainly the number of gallons of water). Too many pool owners have improperly-sized equipment, primarily a pump that is too big (in terms of its horsepower) and a filter that is too small - and often way too small - (in terms of its effective filtration area).
Please also keep in mind that proper plumbing sizes (in terms of the diameter of the pipes) and schematics are also very important, not only for circulation and filtration, but also for chemical distribution, for heat distribution (if you have a pool heater or heat pump), and mainly for safety (in relation to the velocity of water movement through the pipes).
You can read the Pool Manual for additional information about pumps, filters, plumbing, proper-sizing, and proper schematics (layout and design) for all equipment and plumbing.