How are nodes run?

A node is "just" a regular program that happens to use the ROS middleware for most of its input, output and control flow / coordination (ie: callbacks, timers, etc).

So nodes are run as any other program: by starting them from a shell (manually) or from another program (ie: roslaunch).

I wonder how the functions in this file are called when there's no mention of RGBDNode anywhere outside that file.

RGBDNode appears to be a class defined in appliedAI-Initiative/orb_slam_2_ros/ros/include/RGBDNode.h.

Anyone know how int main() in that file is run?

I'm not sure I follow: can you explain what exactly is unclear?

Edit:

The node is meant to be run using, e.g.,

roslaunch orb_slam2_ros orb_slam2_r200_rgbd.launch

but orb_slam2_r200_rgbd.launch calls ths node using

<node name="orb_slam2_rgbd" pkg="orb_slam2_ros" type="orb_slam2_ros_rgbd" output="screen">

If my understanding is correct, it references to a node called orb_slam2_rgbd in a file called orb_slam2_ros_rgbd.

No, the node line looks for a binary called orb_slam2_ros_rgbd and gives the ROS node (ie: the running instance of that binary) the name orb_slam2_rgbd. See also the roslaunch/XML/node - Attributes page.

Binaries (ie: programs, nodes, librarie) can be made up of many source files. In the case of orb_slam2_ros_rgbd, the node comprises two source files which in the end get combined into a single binary. See here for the add_executable(..) call in the project's CMakeLists.txt which configures all of this:

add_executable (${PROJECT_NAME}_rgbd
  ros/src/RGBDNode.cc
  ros/src/Node.cc
)

But there isn't a file called orb_slam2_ros_rgbd or a class called orb_slam2_rgbd.

I hope it is now clear that there doesn't need to be any source file with that name: as long as there is a binary with that name that roslaunch can find (and there is, as it gets created as a result of the build).

There is no one-to-one correspondence necessarily between classes/files and binaries.

roslaunch orb_slam2_ros orb_slam2_r200_rgbd.launch

<node name="orb_slam2_rgbd" pkg="orb_slam2_ros" type="orb_slam2_ros_rgbd" output="screen">