A tingle tanning lotion is one that will get you red in color and give you a tingling sensation shortly after you apply it, by bringing up the blood to the surface of the skin and increasing your micro-circulation, which basically means it gives your skin more oxygen, and by doing so you will be able to tan better and faster, often times helping you break through your tanning plateau.

A more technical definition of a tingle tanning lotion:

A tingle tanning lotion contains an ingredient called a 'tingle' , also called Benzyl or Methyl Nicotinate. Tingle tanning lotions increase the microcirculation in the epidermis, so that more oxygen gets to your skin. Because your skin needs oxygen to tan, the more oxygen your skin gets, the darker you will get. This is how tingle tanning lotions work.