pH -The scientific definition is 'the negative logarithm of the Hydrogen
ion concentration'.
OK - don't give up - its a very important concept.
Lets get through to the definition in every day terms. First accept pH is a scale measuring the acidity or alkalinity of a solution. Squeezed lemon and vinegar are sour or acidic. If we drank them we would take something alkaline like bicarbonate of soda or magnesia to neutralize the acidity in our stomachs - in other words raise the pH.
The pH scale runs from 0 (highly acidic) to 14 (highly alkaline) with distilled water being neutral at pH 7. 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.
pH is the power of a solution to yield hydrogen ions [H+].
The scale between 0 and 14 is logarithmic (pH 8 is 10 times more alkaline than pH 7 and pH 9 is 100 times more alkaline than pH 7)
Now - the scientific explanation of pH as 'the negative logarithm of the hydrogen ion concentration'. Negative because the more hydrogen ions, the lower the pH.