finite means a fixed number of items, a limit, an end.
eg A finite set means a set of items or numbers that has a fixed amount.
D = {1, 2, 3, 4, 5} Set D has only got 5 items, a fixed amount.
infinite means an unlimited amounted of items, no end, goes on forever.
eg A infinite set means a set of items or numbers that has an unlimited amount of items.
E = {positive whole numbers} Positive whole numbers are 1, 2, 3, 4, 5, ... forever