Glitches are sudden changes (usually increases) to the spin rate (the period) of the pulsar. Glitches are usually followed by quasi-exponential recoveries back towards* the initial spin rate. The phenomenon is generally more common in younger pulsars.
The exact mechanism by which glitches occur is not well understood however they are thought to be due to the crust of the neutron star rotating at a slow rate compared with the superfluid interior. Occasionally, the interior couples to the inner crust and spins the star up abruptly.
Unmodelled glitches cause the residuals to drift away from zero, following a quadratic signature. Some pulsars never recover their initial spin-rates following a glitch. Less commonly, a pulsar will 'over-recover', ending up with a longer period than it started with.