Understanding Baud Rate I am new to signal processing and just trying to understand what Baud rate really means. 

As I understand it, the baud rate speed is really the time that the processor takes when it is ON and when it is OFF.  I attached an image as an example.  For a slower baud rate, a 1 is represented by ON and voltage will stay ON and OFF for a long time as compared to a fast rate where the voltage will stay ON and OFF for a short time.

Am I understanding this correctly?

I am looking at transmitting a digital signal over a long distance cable.  The problem I am having right now is I believe the signal is being distorted because it is modulating too fast.  I need the ON's and OFF's to last longer, to stretch out over time. As I understand it this would be as simple as slowing the baud rate down.

Could someone confirm this? Hope it makes sense, thanks.
Yes, that's right.

Even more generally: Usually, we call what you call baud rate the symbol rate, and that is simply how many symbols per fixed time we transmit. The unit is baud [bd], and that's why many people call it (imho, slightly incorrectly) baud rate.

These symbols don't have to be on or off, only. If you, for example, had -3V, -1V, +1V, +3V as the four possible values on your line, than you'd have a bit rate (in bit/s) that would be twice as high as your symbol rate (in bd, or Sym/s), because every symbol carries two bits of information (four values = 2 bits of info, because 2bits = number of options).

Going away from the purely theoretical point of view: for longer links, a simple binary voltage communication is often unreliable, and you might very possibly have to look for other kinds of links that are designed to be used in this scenario. I'd recommend finding a way of analyzing your signal at the receiving end, and making sure you properly terminate that.