When an acid dissolves in water it releases hydrogen ions, H+. This is what makes a solution acidic. Hydrochloric acid, HCl, is a good example: in solution it gives H+ ions and chloride ions, Cl-.
An alkali is a substance that dissolves in water to give hydroxide ions, OH-. Sodium hydroxide, NaOH, gives sodium ions, Na+, and OH- ions in solution. It is the hydroxide ions that make the solution alkaline.
So the difference between an acid and an alkali is which ion it supplies in water. Acids supply H+. Alkalis supply OH-.
