It's called IRC (Internet Relay Chat). It's a "protocol". mIRC is just one of the many client programs available.
http://en.wikipedia.org/wiki/Comparison_of_Internet_Relay_Chat_clients gives a rather big list of programs that can be used and their features. Not only for Windows, but also for Mac OS and a lot of Unix and Linux variants. But, indeed, I see no Android or iOS mentioned.
However, http://www.google.com/search?q=irc+android finds a lot of Android clients. Those might (should?) work on an Android phone or tablet (such as the Samsung Galaxy tab).
And http://www.google.com/search?q=irc+ios turns up http://itunes.apple.com/us/app/colloquy-irc-client/id302000478?mt=8 (and maybe more, but I didn't look) says it works on the iPhone and the iPad. For $1.99 it seems worth a try.
So it was just letting of the m and searching for IRC.
Hope this helps.
I bought my wife an iPad thinking she would no longer be stuck at the desktop computer every evening when she joins her support group friends, a chat group using mIRC. She tried to download mIRC on the iPad and it failed. I could find nothing on the App store or any solution via Google search - no discussions, nothing on point. I did read on Wickpedia that mIRC is for windows operating systems and that is likely the problem. But is there a work around? Please help or at least let me know for sure if no solution exists.