what exactly does it mean to have a probability of 1? And also of 0?

Probability of 1 means that it is certain to happen, whereas that of 0 is certain NOT to happen. OK?

The probability of an event occurring is stated in terms of a percentage of times it occurs. These percentages can range from 0% (meaning the event never occurs) to 100% (it always occurs). Since percentages are equivalent to a number from 0 - 1, you can state this as a number instead of a percentage. For example, if you pull a card from a standard 52 card deck, the probability of it being a heart can be stated as 1 in 4, or 1/4, or 0.25, or 25% -- they are all equivalent ways of saying the same thing.