A strong base is something like sodium hydroxide or potassium hydroxide which is fully ionic. You can think of the compound as being 100% split up into metal ions and hydroxide ions in solution. Each mole of sodium hydroxide dissolves to give a mole of hydroxide ions in solution.
In chemistry, a weak base is a base that does not ionize fully in an aqueous solution. As Brønsted–Lowry bases are proton acceptors, a weak base may also be defined as a chemical base in which protonation is incomplete. This results in a relatively low pH compared to strong bases.
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-).