different colored orbots?

[Perotis]

so what do the different color flight paths mean.  The blue is the one I am currently on and the purple is what the next orbit will look like?

 

http://s259.photobucket.com/user/perotis/media/blahh/Screen Shot 2016-01-02 at 2.04.53 PM_zps69tcmuyb.png.html

[gonzo98x]

Yes

[Xavven]

The blue one is your current orbit, the orange one is the orbit around what appears to be Minmus, and the purple orbit is your resulting orbit after leaving Minmus, assuming you don't fire your engines.

[MaxL_1023]

Those are called "patched conics." Basically, the blue orbit is your current orbit, orange is your orbit after one SOI change, purple is your orbit after two SOI changes.  

When your orbit encounters a planet/moon (Mun, Mimus, the Sun, etc.) by passing close enough (or far enough from Kerbin) the game will change which body is applying gravity to your ship. Assume your orbit has you pass within about 1000km of Minmus. You are then close enough for Minmus' gravity to dominate your path. KSP tells your ship to feel gravity from Minmus as opposed to Kerbin (you only get gravity from one source at a time). Your velocity and position causes a new orbit (usually a flyby, or an open orbit) which is labelled in orange, as you are not on that orbit yet, but will be soon. When the orange orbit leaves Minmus gravity field, you go back to a Kerbin orbit labelled in purple, as it is two orbits away. Notice that it is different from your blue orbit, as Minmus' gravity changed your velocity. The closer you get to Minmus, the greater the change would be. 

 The orange path will only appear if you are going to have an encounter on your current orbit. Watch out if your orbit passes close to the orbits of the Mun or Minmus, as you may eventually encounter them on future orbits. If you don't want this to happen, you need to make sure your orbit passes nowhere near their paths. You might lose your ship - it is quite possible to encounter the Mun in such a way as to hit it. Minmus is less likely, but also possible. An encounter with either of them could also throw your craft hard enough to escape Kerbin entirely, and end up orbiting the sun.

Edited January 2, 2016 by MaxL_1023

[WuphonsReach]

A few links:

https://en.wikipedia.org/wiki/Patched_conic_approximation

A rather informative older thread that talks about why Squad uses patched conics.

And this old chestnut showing the different ways of drawing patched conics: