I just realized people that don't know what these design approaches are most likely are confused by this topic. Here's a quick overview.
1) Start with your main goal. (Build the $50 robot, or whatever it is)
2) Break that goal up into pieces (Electronic, Mechanic, etc...)
3) Further break those down so Mechanic you would put your subsystems such as i) drive system, ii) chasis design
4) Continue from there until you have everything laid out in full detail. Then follow the approach you laid out in order to build it.
So Top-down kinda resembles a pyramid if that's easier to understand.
||||||||||||||||||||||||||||||||||| and so on...
Pretty much the exact opposite of top down. With bottom up you start with the smallest components and work your way up to the ultimate goal of your project.
So an upside down pyramid
Hope this helps.
Here's a link for further reading: http://en.wikipedia.org/wiki/Top-down_and_bottom-up_design