Besides sliders and Civics, research is another thing that happens on a global level in Civilization IV. All the Research Points, or Beakers, that every City collects are put together and used to research Advances. These Advances enable new options for the player, such as new Units, Buildings, Civics, Religions, etc and also open the way to new Advances. As such they move game forwards, from Stone Age to Space Age: the technology tree, which determines the relationships between the Advances and what new options each Advance enables, forms the backbone of the entire game. Once the whole tech tree has been researched, a player still has so-called Future Technologies to pursue: each of these gives a bonus to both Health and Happiness.
Obtaining advances can not only be done through actual research though, that is only one way. Another is through diplomatic exchanges [see Diplomacy] and yet another through Great People [see Great People].
The tech tree itself has undergone one major change compared to earlier games in the genre: where earlier you have to research several prerequisites to be able to research a specific Advance (which led to a very static development of technology), the game now often only requires one of several prerequisites. So rather than requiring both Education AND Guilds as would've been the case in other Civ-like games, Civ4 only requires you to research either Education OR Guilds. There are also no more static eras as in Civ3. The direction a player takes in the tech tree also influences the type of Great People that is spawned. All this allows for a much more flexible tech tree, where players can really specialise in a specific direction and even skip over large sections of the tree if they want to. This leads to much more unique and varied strategies with regard to technology.
For a comprehensive overview of the entire tech tree, see the Civilopedia.