When you use the TRANS function to move population from one of your planets to one of the enemy planets, and you successfully conquer an enemy world using this maneuver, there is a chance for you to gain technology which the enemy had that you had not researched.
First, if there are any enemy ships in orbit over the planet and/or if the planet has any missile bases defending the planet, those will get an opportunity to shoot at your troop transports. This can result in all or nearly all of your troop transports being destroyed before any of them can land on the enemy planet.
If one or more of your troop transports lands on the enemy planet, you will be taken to a ground attack screen which shows how many population you have on the planet and how many population the enemy has on the planet.
You can never successfully conquer an enemy planet which has remaining enemy population on it. You have to kill every last population they have in order to conquer the planet.
If you kill all of their population in a ground battle, you will by definition have at least 1 population unit of your own remaining and you will gain control of the planet.
Ground battles basically go something like this:
The game makes a roll to determine which side loses a unit, every roll will result in a population unit from one side or the other dying. It will never result in both sides losing a unit nor will it ever result in neither side losing a unit.
To determine which side loses a unit, the tech levels of both sides' ground forces will be compared. The chance is 50/50 for equal level technologies. If one side has better technology than the other, that will skew the roll towards the higher technology side not losing a unit and the lower technology side losing a unit.
With large differences in technology, an invading force of 4 units could potentially defeat 100 enemy units.
If you invade the enemy with ground troops and you win, there is a series of rolls to determine if you capture any techs.
If the enemy has only the exact same techs that you have, you will never get any techs this way.
Capturing techs revolves around the factories present on the planet being conquered. If there are no factories on that planet, there will never be any captured techs. There is a limit of 6 techs being captured from one planet, the attacker can never gain more than this number.
The tech rolls go something like this:
For the first up to 25 factories, add 2% per factory (50% total, if they have all 25) and make a roll (50-50 chance, if they have all 25). If you succeed, you get a completely random tech off the list of what the enemy has that you don't have.
If there are remaining factories, repeat this process.
That means if there are 37 factories, you can get 0, 1, or 2 techs. If there are 96 factories, you can get 0, 1, 2, 3, or 4 techs. These numbers will usually skew towards the middle of the range, so with 96 factories you would be very lucky to get 4 or very unlucky to get 0. In that scenario, the expectation should be two.
The implication here is that you probably want to ideally be aiming at worlds which have somewhere in the range of 300 to 400 factories. Pound for pound, that would get you the highest techs per resource sacrificed.
Obviously, it depends on what enemy ships/bases are defending the planet and the stage of the game you are at and so on, but that range will pretty consistently get all 6 techs and it will allow you to conquer small undeveloped worlds potentially in the late game and still get the same 6 techs as if you had conquered huge well developed worlds.
You should absolutely try to do this, because your chances of winning the game increase greatly if you are able to get 6 whole techs for free. That could move you ahead by 100 years of research, especially if the enemy is technologically superior to you.