Why did sailors drink lime juice?

Sailors (especially British sailors) consumed lemon/lime in order to obtain Vitamin C while at sea.

A lack of Vitamin C in the diet causes a condition known a 'scurvy' (which causes your gums to bleed and your teeth to fall out among other things). In olden times sailors at sea for long periods eating preserved food did not get enough Vitamin C in their diets and scurvy was common among sailors. When the cause of scurvy was discovered the navy's of the world began to introduce foods rich in Vitamin C to sailors diets, Lemons and Limes are rich in Vitamin C.