Research Points are the resource used to complete the projected budget of a research project. Each technology is assigned a cost in research points. You are then required to spend money towards obtaining each technology. Research is normally paid for by selecting how much of your per turn income will be diverted to the appropriate laboratories. Each credit you spend on research buys you a certain amount of research points, with the actual amount of research points you get per credit varying due to Faction, researched technologies, and Science Station modules.
Once 50% of the research cost has been spent towards obtaining a selected technology, you begin to have a chance to make a breakthrough in the research of that selected technology. If your feasibility for the technology is low, you may never obtain a technology regardless of how many research points you spend on it.