What is the difference between minimum mode and maximum mode?

Minimum mode in the 8086/8088 provides the functionality of the 8288 bus controller, which means that functions like HOLD, HLDA, WR-, M/IO-, DT/R-, DEN-, ALE, and INTA- come off of the 8086/8088.

Maximum mode means that these functions come off of the 8288, in somewhat enhanced form, and the pins are replaced with new meanings like RQ-/GT0-, RG-/GT1-, LOCK-, S2-, S1-, S0-, QS2, and S21, giving the processor extra capabilities.