tundra010,
Welcome to the PICAXE forum.
The 0V is as mentioned connected to the negative side of the power supply/battery.
It also acts as a common reference for the components in the microcontroller circuits. All signals are referenced relative to the 0V line.
Some integrated circuit data sheets will use abbreviations like Vss and Gnd which as basically all the same thing.
If you have two different voltage sources say as 5Vdc for the PICAXE and separately 12Vdc to drive some motors, then you will generally need to connect the 0V/Gnd of both supplies together. An exception would be with opto-coupled circuits (which you may already know about or learn about later).
Some on this forum (cannot speak for all, without abuse ! ) are endeavouring to give some generic guidance to newcomers on how better present their technical questions in terms of information to provide to gain a solution as rapidly as possible. As such, you may like to have a read at post 4 of this thread for some ideas.
http://www.picaxeforum.co.uk/showthread.php?t=10982