There are 12 (for our our purposes here) discrete notes in western music. These are determined by using really complicated math. Each note corresponds to a specific frequency. A is usually set to 440hz, and A#(the next note on the piano) is usually ~466hz. A microtone would be a note that has a frequency between 440 and 466. Now apply this same concept to the space between the frequencies of all 12 notes.
Instruments like pianos or xylophones cannot normally play these pitches in between because they only have those 12 discrete keys. However an instrument like a violin or a trombone allows the player to smoothly go from one note to another, playing every frequency in between.
When someone is playing “out of tune” they are technically playing microtones
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