The "action" of a guitar is the distance between the strings and the fretboard, normally measured at the 12th fret.A "high action" means the strings are relatively distant from the fretboard, for example 10 millimeters or more between string and 12th fret. (String and top of the fret, not the fretboard) A "low action" on the other hand indicates strings very near the frets,up to as little as 2 or 3 millimeters at the 12th fret.
A higher action, obviously, requires more effort to fret the notes, and the fingers also need to travel more between the rest position and the fretted position. On the other hand, a higher action produces clearer sounding notes.
A lower action requires less effort and finger travel, but beyond some point the string starts to buzz agains the higher frets and produce a "dirty" kind of sound.
Other important factors are the string material and brand, the string construction (e.g. round wound, flat wound, etc), the type of frets, and the quality and curvature of the neck.
Many guitarists, -- especially beginners -- feel that in order to play fast they must lower the action as much as possible.However my suggestion would be to avoid extremes and go for a medium action, one that lets all strings sound clearly in all positions. This will make things a little more difficult in the beginning, but in the
medium and long term it will be much better for you.Finding the optimal action will require some experimentation.Experiment and find a pleasant action, a good compromise between ease of playing and quality of sound. Remember, any real speed
improvement will only come from training, not from shaving a millimeter or two off the action at the cost the quality of your sound.