Simply put, guitar action that we're talking about is the distance between the guitar strings and the fretboard. It could be set up improperly and affect your guitar playing.
Low action means that your strings are closer to the frets while high action means further away from the frets. Preference varies when it comes to the guitar action people want.
High Action & Painful Fingers
Higher action will take more strength to press the strings down to the frets, making it difficult to hold chords. This is painful on the fingertips and will slow down your scale speed on guitar. But it will accommodate more aggressive playing techniques and produce cleaner sound, which is better for harder strike and studio recording.
Low Action & Fret Buzz
Low action enables quicker note-playing as it takes shorter distance to press the strings to the fret. You will need less time to react between different notes. However, low action might cause fret buzz.
Fret buzz is the rattling sound the string produces when it hits the fret. When guitar action is low, your string will touch the fret because it vibrates during playing. But you'll be fine if this sound doesn't affect the play when plugged to amp. That is why electric guitars typically have lower action than acoustic guitars.