Why are pickles sour?

Short answer: The human tongue detects anything that is acidic as sour. Vinegar is acidic, and pickles are cucumbers that soaked in vinegar.

Vinegar has a pH around 3 but varies around the type of vinegar you're using. Cucumbers are 95% water and when you put a cucumber in a jar of vinegar, it soaks up all the vinegar and becomes a pickle. So therefore when you eat a cucumber and taste the sour, you are tasting the vinegar inside of the cucumber.