watmm: XA is a system for supporting transactions across systems. So if you have some rows to modify in MySQL, and also some rows to modify in MSSQL, and also some file to write to tape, and you want all of that done together or not at all as one big transaction, you use XA. The doublewrite buffer is a file flushing technique that makes it so that InnoDB is more crash-stable.
doublewrite is basically somebody gives you a phone number, you write it on your hand, and then you go and copy it into your phone's contact list. If you drop your phone and it breaks before you get a chance, you can still go look at what you wrote on your hand and enter it into your new phone.