What is a protocol? And what does "Open protocol" mean, then?
Roughly speaking, protocols describe the underlying mechanism of exchanging data between clients (the programs you use for chatting) and servers (these care about all the backend stuff).
Without protocols, your chat program wouldn't understand what your friend's program just sent to your PC, let alone all the necessary communication in between.
So... what about "Open protocols"? And why should I care about the openness of such stuff like protocols?
The main reason to use open protocols is freedom. They neither tie you to a specific program that is only available for one or two platforms nor do they force you to have an account (and accept a contract) with a particular provider.
With a closed platform it can happen that you have to run a bloated client on your old computer. Maybe you don't like the look and feel of the program, maybe it has annoying ads that eat lots of screen space, or you'd like to run the client on an uncommon platform which isn't supported by the provider.
In these situations, you usually don't have other choices rather than using the official application (if at all). Maybe you are lucky and there are third party applications (most likely developed using reverse engineering) that meet your needs. But these applications most times have less features than the original client and may not work properly because the developers haven't got access to the information about the inner workings of the protocol. Even worse, the provider could change the protocol, breaking non-official applications.
With an open protocol everything is different. Developers can create applications without having to get the authorization of a company. Furthermore, having full access to the protocol documentation and therefore to the inner workings of the system enables them to develop better applications. Users aren't tied to any program; if one doesn't fit their needs, they can just change to another one. All developers have the same opportunities to improve their applications.
So, even as a regular user (who is not involved with creating applications), you benefit from the “openness” of the underlying protocol your chat program is based on.