A base is a solution that contains more hydroxide ions than hydrogen ions. Common household items that contain bases include baking soda (which contains Sodium Bicarbonate), ammonia (which contains Ammonium Hydroxide), and drain opener (which contains KOH and NaOH).
A strong base is a base which is fully ionized in solution. Here are some examples:
Weak bases are only partially ionized in solution. Here are some examples: