One common case is "che cosa", for example che cosa stai cercando? cosa stai cercando? che stai cercando? are all correct sentences of almost identical meaning. In the first case "che" means "quale" (which/what) and is an adjective. In the last means "what" and is a pronoun. Another case is "che" as a conjunction introducing a subordinate clause. In this case it means "that". Penso che tu troverai la strada facilmente Penso troverai la strada facilmente The second form is less common but is also used, in particular in spoken language. One last case is ché as a short form of perché. Preparati ché è tardi In this case could be omitted, in written form, using colons Preparati: è tardi There are few other cases like è più azzurro che verde (more blue then green) but less common and very specific.

It usually means /that/, or /il quale, viz.: who/; usually it cannot be omitted, although it may be omitted in English. Mi ridai il libro che ti ho prestato ? You can't omit /che/ here.

Perhaps you re thinking of "che" in "che cosa" (what?)... In this case, "che" can be omitted.