IIR filters are the digital equivalent of analog filters — they use feedback loops where the output feeds back into the input. This allows very efficient filter implementation with low latency. However, IIR filters cannot achieve linear phase — different frequencies experience different delays, which can alter the timing of transients.
Most parametric EQs, high-pass/low-pass filters in DAWs, and crossover filters use IIR designs because of their efficiency. For applications where phase linearity is critical (mastering EQs, precision crossover), FIR filters are preferred despite their higher latency.