Digital audio relies on a precise clock to determine when each sample should be converted. Jitter is timing uncertainty in that clock. Even nanosecond-level jitter can cause measurable distortion. Audible effects: flattened stereo image, reduced HF clarity, and increased background 'graininess.'
Modern audio interfaces use high-precision crystal oscillators and phase-locked loops (PLLs) to reduce jitter to inaudible levels. External master clocks (used in large studios with multiple digital devices) ensure all converters share the same timing reference. For home studios with a single interface, the internal clock is sufficient.