There are two principle reasons to evolve your pokemon.
The first is base stats. Almost without exception, an evolved pokemon's base statistics, that is to say, ATTACK, SP. ATTACK, DEFENSE, SP. DEFENSE, SPEED, and HP are higher than its previous form. This translates to an immediate boost in battling abilities.
The second is that pokemon movepools often expand with evolution - the pokemon is able to learn abilities it would otherwise not be able to (often related to its new type, if applicable). While generally speaking, non-evolved pokemon learn attacks earlier than their evolved counterparts, it is not always true, and depending on the individual scenario, their may be no reason to delay evolution.
Additionally, if the move in question is learn-able via TM or Move Tutor, it can be unnecessary to wait until a certain level in the first place - you're just missing out on the higher stats at that point.