I want to know what purpose does console solve in sublime text 2. This is invoked by pressing Ctrl+Shift+`
Is this a kind of debugger, or It just helps you to install packages.
Sublime Text 2 has Python embedded, and the console let's you inspect the current editor state, and create python code directly in the console to manipulate that state. See the API reference to see what you can do.
Sublime Text 2 extensions are thus written in Python, and any logging they do ends up on that console as well. So indeed, you can see the console as a debugger as well, if there are any python exceptions they'd be printed to that console.