Low and Slow is cooking at a lower temperature over a longer period of time. This helps to break down collagen found in connective tissues of meat to yield pull-apart, juicy and tender results. We often refer to this as 'indirect cooking' where charcoal or wood is placed to one side of the BBQ and food is cooked on the other.
Hot and fast cooking involves grilling food at a hotter temperature for a short period of time such as skirt steaks and vegetables. This is called 'direct' cooking where meats and food are cooked directly over hot charcoal or wood.