Wow, people these days are completely funny.
Complicated explanation:
Hacking is basically modifying any part of the system/software to work differently to what it's intended to, usually for a good purpose, like making a script that moves the cursor every 59 seconds to prevent screensaver (e.g. watching a movie). For some reason it's been developed into this term describing people breaking into other people's accounts and servers and whatnot.
Of course, it's possible to break into someone's computer through the internet. This guy could somehow gain access to the "xat" server data, break through all the passwords and security that will inevitably be there, decrypt the information using the decryption key only the xat staff know, take the history of connections which may not even exist, search through gigabytes of data to find your username and match it with an ip address, access your computer through that ip address, send an unauthorized uncertified script onto your computer, somehow get that through firewall, router (if you have one), proxy (if using one) and your ISP, then somehow remote-control your computer from his.
And finally, get sent to child rehabilitation for a few years.
Simple explanation:
The guy is a complete computer noob if he thinks he can do stuff like that. I see two possibilities here. #1 is that he tries to scare you, which seems to have worked but definitely won't work again. #2 is that he'll spend half the day looking for a free easy solution on the Internet but will fail epically.
Finally, a note:
Do NOT give away any of your personal information because with that it makes it easier to break into your account (which is infinitely easier than breaking into a computer). Many sites have "recovery questions" which if other people can answer they can get your email account, and through that into many other accounts which you used your email to sign up for.