Oversampling runs the internal processing at a multiple of the input sample rate (e.g., 4× oversampling processes 44.1 kHz audio at 176.4 kHz internally). This pushes aliasing artifacts far above the audible range and allows gentler, better-sounding anti-aliasing filters.
Many plugins (especially compressors, saturators, and limiters) offer oversampling options. The trade-off: oversampling uses more CPU and adds a small amount of latency. For critical processing (mastering limiter, saturation), oversampling dramatically improves quality. For basic tasks (EQ, gain), it is unnecessary.