Simply put, a Full System allows you to pick more than just the allowed 6 numbers for each lotto game. For instance, a "Full System 7" allows you to pick 7 numbers, while a "Full System 8" allows you to pick 8 numbers, and so on. The highest amount of numbers you can pick is 20 which is a "Full System 20".
In a FULL System, your entry is equivalent to playing every possible 6-number combination from your selected numbers. For instance, if you played a Full System 8 (which has 28 possible combinations), your entry is equivalent to playing all 28 possible combinations of 6 numbers from your 8 selections.