discrete - data that can only be particular numerical values, e.g. the number of TV sets in a house (could be 00, 11, 22, 33 but not values in between like 1.31251.3125).
continuous - data that can take any value in a range. Variables such as heights, weights and temperatures are all continuous. For instance, someone could have a height of 172172 cm, 172.4172.4 cm, or 172.215172.215 cm (if it can be measured accurately).
Categorical (qualitative)
ordinal - data that has natural, ordered categories (high achievement, satisfactory achievement, low achievement)
nominal - data that requires sub categories (hair colour --> brown, red, blonde, black)