Each village has its own set of researched discoveries. There are three types of research that can be done in each village, and there is a specific building where each type of research is done. Discoveries made in one village cannot be used in another village; they must be researched in each village where they are wanted.
The first type of research is that of troop types, which is done in the Academy. After constructing the prerequisite buildings for anything other than the basic infantry units, the new unit must be researched before any can be made. This is a one-off resource cost, but rises to quite high level for more advanced units.
It is not necessary to research all possible units; nor is it necessary to research units in any particular order. There are no "prerequisite troop types", and no "technology tree".
The other two research types involve improving units' attack and defense statistics. Attack improvements are researched in the Blacksmith, while defense is researched in the Armoury. These improvements are made on a per-troop-type basis, and have a "level" from 1 to 20 for each unit. Thus, for example, a village may have researched level 3 Swordsman offensive improvement (weapons), level 4 Phalanx defensive improvement (armour), and level 2 Pathfinder defensive improvement (anti-scouting).
Blacksmith and Armoury research applies to all units of that type which are supported by the village in question, regardless of whether a particular unit was built before or after the research.
The improvement in attack or defense is 1.5% per level, cumulatively (i.e., a unit's statistics are given a multiplier of 1.015^R where R is the researched level), with the maximum improvement being 34.7% at level 20.
The advantage of researching improvements, instead of spending the resources on additional troops, is the ability to increase the power of one's army without increasing its upkeep cost. This is extremely important in the late game, when upkeep cost becomes the true limiting factor on military power. However, it requires hundreds of troops before researched improvements "pay off" by providing more power than would have been obtained by spending the same resources on more troops. This means it's not a good idea to pursue this sort of research in the early game.