Debug-mode refers to running an application in a way that allows debugger to be attached to it. The debugger allows the application developer to perform stepping through the code, inspecting variables and other actions. These actions are known as debugging, usually used when developing application or tracking bugs. For example to run a java application in normal mode you would use
"java Main.class"
To run the same application in debug mode you would use
"java -agentlib:jdwp=suspend=y,transport=dt_socket,address=8123,server=y Main.class"
this will cause the application to listen on port 8123 for debugger to connect to it.