I'll give you a non-technical answer, but enough info to get a feel for what callbacks are and how they relate to threading. I'm sure you can get many details from google though.
Callbacks are functions that are called when a pre-define event happens in the computer. When you setup the callback you tell the computer what that event is. It could be an electrical signal on an input connector, and counter or clock signal reaching a preset value, or in the case of ROS a common use of callbacks is for receiving messages on a specific topic. In all these cases something has happened and your program needs to respond. So if you have a callback setup for a signal that arrived on a pin indicating a sensor has new data, your callback would likely communicate with that sensor to get the data it has. Deeper in the code you could say the the signal generated an interrupt and that led to the callback being called, but that applies for the case of a signal on a pin from a sensor. Callbacks can be triggered in ways other than interrupts, so I won't go deeper. In ROS, if a message has arrived on a topic, your callback should read the message and process it.
Threads are blocks of code or functions running in parallel with other functions or blocks of code from a program. A single thread program will run it's code through the processor single file. One function, then another, then another, as it works it's way through the program. On a multi-threaded program, it can fork the program into different threads and run multiple functions together, and the leave it up the operating system on how to manage it. This can be beneficial if your program has to do two things that don't need to sync in time - say read data from a temperature sensor and also play a song from memory. Those two things have nothing to do with each other so you may want to do sensor reading in one thread while playing music in another.
Threading and CallBacks - they are related in that they both involve processing blocks of code or functions. Callbacks can be called in the primary thread of a program, interrupting that main program, or they can be called on a different thread so the callback is processed while the main program continues to run. Different programming languages many handle default callbacks in different ways. So if you get to the place where you need to really understand exactly what is happening, a little research will be be required for the setup you're using.
http://wiki.ros.org/roscpp/Overview/C...
