Educate me please?
 

So it was 88 here in Oklahoma so we decided to take the boat out. I have been tearing through (literally) my boat cleaning it and learning as much as I can. In the process I disconnected both batteries and moved them to clean out the engine compartment. Apparently there was a wire I forgot to reattach because I was that guy on the ramp that couldn't get his boat started. After a couple of minutes of cranking I thought I would check to see if I missed something. Behold there was a stray wire so I attached it to the positive of the battery, cha ching, she fired right up. I traced this wire back, to what I'm not sure but there was a splice about 3 inches off of the component and the original wire was purple I do believe. So we cruise out and decide to stop turn off the key and pull it out but the engine is still running. I went to the engine compartment and removed this wire that I fastened to the + terminal and the engine cuts out. All of that to ask what does this wire go to, and where should I affix it. I assume it should get power when the key is in run, but I am pretty sure that it was not ran all the way up to the ignition switch? Sorry for the length. I look forward to you all making me much smarter.