From what you have said I dont think you need to create functions etc.
The string you gave earlier looks like user details, perhaps part of this integration is to create / auto update users? It may help if you explain specifically what this integration does?
What I think you need to do is enable standard web services of which there are many if you scroll down this page:
That involves creating a user account for the remote application, assigning it permissions and generating a token. The remote application then "logs in" as this "user" To control bits of moodle like creating users, enroling users on courses etc.
For that you would not need to create functions, just use the ones in the list linked above.
However, if the integration goes the other way and you want to get Moodle to send information to the other system you would as Tim said need to write (as in programming) a plugin to detect an event in Moodle and call the web service in the remote application. If this is a commercial product which integrates with Moodle you would normally expect them to provide the plugin to all their customers.