Research structures are special buildings that can be constructed on foundations and in some cases at space stations. These structures have a number of research slots or research points that can be applied to a given technology and over time will 'learn' the Technology or unlock the upgrade indicated.
Researching is the act of applying research points of the research structure to an indicated technology or upgrade. You can apply sum or all of the available points to any technology and the structure will begin researching aka learning.
If you apply research points to a technology that has unmeet requirements the researchers will 'study' the requirements first thus you can indicate a long term research goal and let the researchers sort out the order to research in to achieve said goal. You can have multiple research structures and you can apply all research structures to the same goal increasing the rate at which the goal is reached. Its often handy to give each structure a unique long term goal that is related to other efforts thus speeding up the research of requirements mutually benefiting each other but resulting in the completion of multiple long term goals.
Researchers are a type of item that can be bought or more accurately hired; they incur a maintenance cost but boost research rates of the research structure they are applied to. Researchers always cost even when they are not researching and so its wise to dispose of them when not in use. Researchers have no facilities so you will need to assign them to a facility before they can benefit your research operations, again they do cost even when they are not assigned to a facility.