The TLDR of XAI is that you can "see" (or think you see) how features influence the decisions of your models. For example, if you have a sentence "buy this pill to get skinny!!!!!" and you try to classify if it's spam, the "!!!" might be marked as very spammy. You often find it by masking the "!!!" and seeing that now the message is maybe not classified as spam (often you look at the output dist). Of course, there are many more sophisticated methods to do so and there is a lot of impressive work, but it's the TLDR.

There are many explainability methods, it's a very hot topic. It might be yet another paper, or not. The title makes no sense at all, there are gazillion explainability methods for transformers. I am sorry, I did not read all of the paper so I should probably not talk too much. It just looks very similar to things I already saw.

Generally speaking, you should start using XAI if you do ML, if you do NLP - look into the proven methods, e.g. SHAP and LIME first. If you work with trees, look into TreeSHAP. If you work with vision, look into what I shared here. Sorry if my preceding comments were inaccurate but I hope I still provide some value here :).