There are three types of research/tech system that can be used on worlds.
The Simple research system is the most frequently used setting. The 3 level system is also used fairly frequently. The 10 level system is extremely rare, and only used on a couple of worlds.
Village tech levels are preserved when they are conquered and when they are barbarian.
Simple research system
Unlike the other two research systems, the Simple research system only allows units to be in two states: Not researched, and Researched.
It is only possible to train units in a village if they have been researched in the Smithy. However, the fighting power of the units is not affected by research, since there is only one possible level of it.
It is not possible to downgrade the research of a unit.
3 level system
This research setting is also sometimes referred to as the '15 tech system', due to each village only being able to research a total of 15 times.
Each unit can be upgraded up to a maximum level of 3. At level 1, you are given the ability to train the unit. At level 2, they will be 25% more powerful in battle. At level 3, their bonus will increase 40%.
Since you can only have 15 active research levels in a village, you will need to carefully choose what units to research. It is possible to downgrade research levels all the way down to not researched.
When stationing your troops in another players village as support, troops will fight at the tech level of the village they are stationed in, NOT the village they were sent from.
10 level system
The 10 level system is similar to the 3 level system, but allows each unit to be upgraded to level 10. The higher the research level, the better the unit performs in battle. There is no limit to the number of researches you can have in a village.