I read the following statement somewhere on the web: "Every blockchain address possible already existed, long before a wallet found it. The reason is that blockchain addresses are the result of a mathematical operation." Can somebody explain this to me as they would to a child. I have no computer science background.
An address is an encoding of a 20 byte value. This value is just a number, from 0 to 2^160 (there are 8 bits in a byte, so a 20 byte value has 160 bits and a bit can be 2 values). Because we know what all of those numbers are, all possible addresses are known beforehand and already exist; they are just a number.
I would argue that the wording of that is so poor that it should be considered incorrect.
Yes, an address is a result of a calculation. However all numbers can be the result of a calculation. The quote you gave could be paraphrased "all addresses already exist because addresses are numbers, and numbers exist". Phrased this way, it's easy to see that the quote contains no useful information, and is potentially misleading.
As Andrew said, first you choose a number between 0 and 2^160 (inclusive). (1 byte has 2^8 combinations, so 20 bytes is (2^8)^20, 2^160). Then you (or, the software) calculate corresponding private key, then the public key and the address. So theoretically, a computer can find all BTC addresses. (But that's actually impossible - https://www.reddit.com/r/Bitcoin/comments/1rurll/on_the_subject_of_listing_all_possible_private/)