Perhaps an example would be best.
Suppose you do not convert the miner and do not build other colony ships as you research. So, you have only two colonized planets. No matter how many research points you generate, you will not be able to gain more than three research techs per turn.
Thus, suppose you began with a run up the Interstellar Government tech path and are generating by the end something like several hundred points per turn. Say you now switch to Space Militarization. A simple counting of research costs would say that you would gain in the next turn Space Militarization, Space Weapons, Rail gun theory, basic rail guns, enhanced rail guns, and maybe another level or two.
You will NOT gain them all. You will advance only N+1 levels which, since you have two planets, means you will gain only three levels. The other points disappear.
This is another reason to convert the miner to a colony planet and to quickly get three (or more) planets colonized when you are using a high research strategy and before you shift from an initial tech path to the start of another.
(If you use your initial colonizer as an extra scout, or are simply determined to save it for a real juicy planet you have not yet found, having only your home world colonized will limit you to two per turn)