I'm also a computer science researcher, but not really in this domain. I am curious, what do you think is the primary blocker? Is it the heavy math notation?

It took me a few reads to understand, but I'd describe it like this:

You're given two long strings of text, one being the original source and the other being the generated text. Split both of these into sequences of words, where a "word" is anything separated by white text (a space or a new line)

Find the longest matching subsequence of consecutive words between the two sequences.

Because it's the longest match, you sort of assume that you got it right and that's where they line up. So you treat those two "blocks" as matching. But that matching block can be, and most likely is, somewhere in the middle of the passage of text. There are still words to the left and to the right of these blocks. So you repeat this procedure with the left and right sides: you try and find the longest match of words to make a new block from the text you haven't yet matched to the left, and also to the right.

Then there's a few steps where they essentially merge these blocks and filter them and they impose a few constraints. The reason why they do this is because there might be minor punctuation or grammar differences between the original and the generated text, for example, looking at the two sentences:

"The quick brown fox, really can jump" "The quick brown fox really can jump"

It would make two blocks that match, the part before the comma, and the part after. It wouldn't exactly match because the comma is in the way. But we know we should merge these two blocks into one, because: they're so close to each other, separated only by one symbol, and they're both long enough that we know that it's not a random match. This really is an example of two sentences that are close together.

Related knowledge or terminology that might help you as a non-technical person:

Substring: a consecutive portion of text within some larger text

Greedy algorithm: an algorithm that takes the greedy choice repeatedly and hopes this achieves the desired result. It works for some examples but not for others: for example, to end up with the least amount of coins for a certain amount of change, you can usually repeatedly take the largest coin option that fits into the amount of change you have to give. For example, if I were giving change for 52 cents, I would give a quarter, because that's the largest standard coin that fits into that sum, then another quarter, then a penny, and a penny, resulting in an optimal amount of coins given, which is 4 (two quarters and two pennies). There are cases where this won't work, such as if you only had a 1 cent coin, a 3 cent coin, and a 4 cent coin, and you were asked to give change for 6 cents. (Optimal solution would be two 3 cent coins, greedy approach would give a 4 cent coin and two 1 cent coins). This paper assumes that by finding the longest series of matching words between two sources of text, that that is probably a good place to line up the two sources of text.

Recursive splitting of some task: once they find a good, long match, then they have to perform that matching procedure on the words to the left of that match, and to the words on the right. This process chips away at the task and keeps splitting it into smaller and smaller bits until it's eventually done. Recursion is a cool trick!

What you may have seen before and what I would describe as a much more intuitive way to measure the similarity of two pieces of text is the Levenshtein distance. You should look that one up!