We investigate a mean-field version of Bank--El Karoui's representation theorem of stochastic processes. Under different technical conditions, we established some existence and uniqueness results. As motivation and first applications, the results of mean-field representation provide a unified approach for studying various mean-field games (MFGs) in the setting with common noise and multiple populations, including the MFG of timing and the MFG with singular control, etc. As a crucial technical step, a stability result was provided on the classical Bank--El Karoui’s representation theorem. It has its own interests and other applications, such as deriving the stability results of optimizers (in the strong sense) for a class of optimal stopping and singular control problems.