The Agent Compatibility Matrix in the CI Server Settings section contains a table with all Agents as column names and all Configuration Stages as rows. The intersecting table cell contains the compatibility result for that Agent and Stage. The following image shows a typical compatibility matrix.
The 
imagine means the Agent can run that stage.
The 
image means the Agent cannot run that stage.The * imagine means the Agent can run the stage but won't be able to use source code found in any of the non-default branches in the repositories attached to the Configuration.
Incompatible Agents
The reason an Agent is incompatible with a stage is displayed when hovering over the . In the following imagine, I've hovered over the incompatible imagine for Build stage in the todotxtnet project's Release configuration on Agent continuagent.
...
The tooltip that pops up shows a list of properties the stage requires but the Agent doesn't have. In this example, the stage requires access to the MSHTML and Git executable. Since those executables don't exist on continuagent the stage cannot be selected to run on that agent.
Semi-Compatible Agents
A semi-compatible agent is one where there's an asterix next to the tick *. This can only occur when you have a repository attached to the Configuration that uses distributed version control. Currently they are, Mercurial, Git and Subversion (Branch Aware). If you're using one of these repositories then it's possible for a stage to use multiple branches in that repository. This means, when the stage executes on the Agent, the agent would need to switch branches using that repository system's executable which means it needs it installed. If you don't need to switch branches in the stage then the agent will execute it without any problems otherwise it will fail.