Cents are the units of tuning accuracy. A cent is one hundredth of a semitone. Since there are 12 semitones in an octave, there are 1200 cents in an octave.
Every tuner has manufacturer specifications for accuracy. They describe how accurate the tuner's internal pitch reference is, and therefore how accurately you can tune your instrument using their product. In simple terms, the lower the inaccuracy in cents,and the finer the display, the better the tuner. Rack tuners often have the capability to display tuning to the nearest cent.
It is commonly agreed that the human ear can notice a pitch change of about five cents; no guitar or other musical instrument will ever be perfectly in tune, but less inaccuracy in the tuner allows tuning near enough to perfect that no listener will be able to hear the difference.