Research is a way of improving the abilities and stats of units and buildings.
Types of Research
0 A.D. has three types of research: Phase Upgrades, Technology Pairs and Single Technologies.
By far and away, phase upgrades are the most important research items. They're equivalent to age upgrades in Age of Empires (ie. Dark age to Feudal Age.) Phase upgrades unlock new units, buildings and technologies. In addition to having a resource cost, phase upgrades cannot be researched unless a player has enough buildings in that phase.
In most games, players start in the Village phase and can the upgrade to the Town phase and then to the City phase.
Phase upgrades are available at the Civilization Center.
You may choose only one option out of two. The other is blocked for the rest of your match, so you should adapt it to your strategy.
Unlike technology pairs, single technologies don't block other research.