A strong base is a base that breaks apart 100% in solution. For example, if solid sodium hydroxide (NaOH) is placed in water, the solids will completely break apart into equal amounts of sodium ions (Na+) and hydroxide ions (OH-).
A weak base is one does not break easily in solution. For eg. HCl-Hydrochloric acids, Nitric Acid-HNO3, Sulfuric Acid-H2SO4.