An alkali is a soluble base. Sodium hydroxide, potassium hydroxide and calcium hydroxide are alkalis. When an alkali dissolves in water, the solution contains hydroxide ions, OH-, and has a pH above 7.
All alkalis are bases, but not all bases are alkalis. A base that does not dissolve in water is insoluble, so it cannot form a solution containing hydroxide ions and it is not an alkali. Copper oxide is a base that reacts with acids, but it is insoluble in water, so it is not an alkali.
To decide whether a substance is an alkali, ask two questions. Does it react with an acid to form a salt and water only? If yes, it is a base. Does it also dissolve in water? If yes again, it is an alkali.