Status Effects are (Normally) Conditions that can affect your Pokemon in different ways. Commonly known examples are Poison, Sleep, and Paralysis. Status Effects are usually caused by the Opponent's moves, Ex. the move Toxic may cause poisoning, Sing may cause Sleep, And Thunder Wave may cause Paralysis. Status effects may be Lifted or prevented by moves like Refresh(Lifts all Status Effects), or Safeguard(Prevents status Effects for 2-5 turns), Or abilities like Natural Cure(Heals status effects when switched out)Or Limber(Prevents Paralysis) Most status effects are kept after battles end.
A complete list of Status Effects and what they do: Poison: Pokemon loses some HP each turn, Poison types not effected, Paralysis: Pokemon is slower then normal, and may not attack, Asleep: Pokemon cannot attack for 2-5 turns, Burn: Pokemon loses some HP each turn, Fire Types not Effected, and Frozen: Pokemon cannot attack for 2-5 turns, will be thawed out/returned to normal if either it or it's opponent uses a fire move.(Note: if in a double battle, and on opponent uses a fire move against the one that isn't burned, It won't be thawed out) There are also other Status Effects that are negated if the pokemon switches out, or if the battle end. Confusion, Cursed, Leech Seed, Nightmare, Attracted are among these.