The scientific definition is 'the negative logarithm of the Hydrogen ion concentration'.
Lets get through to that definition in every day terms.
Squeezed lemon and vinegar are sour or acidic. Now instead of sour, lets use the term 'hydrogen ions', and instead of alkaline lets use the term 'hydroxyl ions'. Vinegar has many more hydrogen ions than hydroxyl ions. Conversely, soda ash and bicarbonate, being alkaline, possess more hydroxyl ions than hydrogen ions. In summary, acids produce hydrogen ions, alkalis produce hydroxyl ions.