Good question, I should have explained that in my profile.
To do science, you have to get a degree, and then you do a PhD. PhD stands for “Doctor in Philosophy” (which is a bit stupid since a PhD in science really doesn’t have anything to do with Philosophy!), so people call it a doctoral degree. That means that when you get a job after your PhD, it’s postdoctoral, in other words it’s after your doctoral degree (‘post’ means ‘after’ in Latin). And ‘fellow’ is a word used for someone who has a job at a University (or in my case a research institute) – why they use the word fellow, I have no idea! So being a postdoctoral research fellow means that I have a job at a research institute after having done my PhD.