A spell which has a somatic spell component is one that requires some form of arm or hand gestures to perform. a caster must have at least one hand free to provide a somatic component.
Arcane spellcasters attempting to cast a somatic spell may suffer arcane spell failure from wearing armor. This can be eliminated with the still spell metamagic. Bards and Warlocks suffer no such spell failure while wearing light armor, and these two classes can also take the Battle Caster feat in order to extend this to medium armor as well.