Here is a thread list of some of the more commonly encountered third party programs. It's not an all-inclusive list, as new ones are being developed all the time, but it might give you and idea of the types of things that are considered "malicious third party programs." Basically, it does not have to be a scripting program. It can be any sort of program that directly or indirectly interacts with League in a manner that has the potential to give the player an unfair advantage over other players.
One example I like to give people is how Curse Voice was originally released. It contained timers for a player's teammate's ultimates. At that time, the client did not have that information clearly displayed and Riot considered it to be an unfair advantage for the players who used Curse Voice vs. the players who did not. So it was considered one of the banned third party programs at that time. Curse modified it to remove the timers, and once it was re-released, Riot approved it for use. There are many, many other types of programs that are considered banned. Some are for scripting, some are map hacks, some are timers, there are even certain gaming keyboards/mouses that I have heard of that are potentially problematic because of the types of macros and software they use. Using macros to cast multiple abilities with a single key can even be counted under this category. It is a very broad term.
Unfortunately for the players who receive the bans for third party programs, it can also be a very frustrating one. The groups that develop the hacks and cheats can be quite clever at making their programs, and one thing Riot does not wish to do is let them know how they have discovered them. So, when any player is banned for the use of third party programs, that player is told what the ban was, but not the specifics of what the exact third party program was, or how it was detected on their system. It makes it almost impossible for the cheaters to know how they were caught, but unfortunately, it also makes it very difficult for the innocent players, or the unwitting players, to know how to begin defending themselves.
The only thing I can suggest is that you go through the list, and try to see if there is anything there that rings a bell. You may also want to think back and see if there are any times when you may have logged onto anyone else's computer to play, as if they had any programs on their computer, it could have triggered the system for your account. Also, if anyone else has had access to your computer, you may want to check with them to see if they have downloaded or installed any programs onto it without your knowledge.
This is not the easiest situation to exonerate yourself from, but it is not impossible. If/when you submit a ticket to Player Support, try to be as polite and patient as possible. I'm sure it's a very frustrating situation, but it will not help your cause if you snap at the Support Specialist. It may take a few different tickets or attempts at contacting support. Be prepared, many times they have to tell you that they have reviewed your case and are confident in the analysis of the system. And Riot's system is very good at detecting things. What you have to do now, is try to figure out what it detected, so that you can prove to Support that it wasn't used for cheating.