IRR is the time-weighted annualized return on an investment or fund. Unlike MOIC, IRR rewards returning capital quickly: doubling money in 1 year is a 100% IRR, while doubling money in 5 years is about 15%. LPs use IRR alongside MOIC because the same MOIC can imply very different actual investor experiences.
IRR is sensitive to early distributions and to large recent marks. A fund that returns capital quickly through an early exit can show extraordinary IRR even if total MOIC ends up modest.