Pokemon Rangers are part of a governmental organization whose job is to protect the environment, the wild species that inhabit it and occasionally providing assistance to citizens who need it. Imagine a park ranger and a cop combined together - that's basically what they do. They use pokemon to help deal with or prevent ecological disasters, fighting off criminals who use pokemon for ill intents and even arresting pokemon poachers. In Pokemon: Rescue Rangers, I remember seeing a few of them distributing newspapers and delivering goods around a village as one of their side-jobs, because the place was somewhat isolated and people needed help with certain services in order to have a functional community.
Rangers and Trainers are different "professions" so per se - while any kid can become a trainer (assuming they have a pokemon) in order to become an official ranger they first have to graduate from the ranger academy. Only then they're allowed to have their first (and only) pokemon partner, whom they bond for life. Unlike trainers, who can have up to 6 pokemon in their party (and capture many more), rangers can only have one but are allowed to temporarily "capture" more depending on the situation, for example: a wild houndoor has been causing trouble in an area by harassing endangered species and starting small fires near a human settlement. The pokemon ranger can capture said Houndour and release him in a different location where he can still be happy but no longer poses a threat.
Rangers don't use pokeballs like Trainers do, instead, they use a device called "Capture Styler" - its basically a remote control that also has a built-in communication system and other utilities, like the Browser (Ranger's version of the Pokedéx). When a ranger wishes to command a wild pokemon, the Styler releases a small disk that, when in close proximity to its target, emits "friendship signals" that temporarily pacify pokemon into submission. As for what place this career would have in the game, well... If a particular organization were to go after endangered (and protected) pokemon simply because they're rare... or if some individuals were to use pokemon to conduct illegal practices, then I'm pretty sure a Ranger would step in to prevent that. Its their duty after all! ;)
That's basically the gist of it! Hope it was helpful. :P