The Tech Web is a new way of looking at Research within the game, but to get the most out of it, the Tech Web does require a little bit of advance planning, especially if you want to take advantage of building Wonders, or if you are aiming to get XP for a single Affinity quickly in order to achieve an Affinity Victory.
Technlogies are linked by lines, and in order to research a technology, you need to have researched technlogies so that they create a linear path to it. Technologies can have "sub-technologies", and there can be as many as four assigned to each technology. After the main technology has been researched, the sub-technologies can be researched in any order.
Both technologies and sub-technologies can grant access to Affinity XP, Buildings, Tile Improvements, Wonders, and certain Victory Condition routes. At-a-glance, Buildings can be identified with a half-octagon. while Wonders can be identified with a semi-circle. Affinity XP is designated by the appropriate coloured icon for that Affinity; Blue for Harmony, Red for Purity, and Yellow for Supremacy. In order to work a specific Strategic or Affinity resource, the technology that unlockes access to it must first be unlocked. Basic resources may be worked off-the-bat.
Some technologies provide such a benefit to playing, that it is arguable that they are unskippable (or rather, that is it highly adviseable *not* to skip them). One such technology is used to construct Colonist units (that are able to found Outposts, that later turn into fledgling cities), another gives workers immunity to the toxic Miasma, while still another allows land units to "embark" (travel) on water.
It's also important to note that, even if you research a technology that allows you to build an Affinity Victory Wonder, it will not be available unless you have the appropriate amount of Affinity XP, which will require researching more technologies within the web.