Let's talk about waveguides. The lowest frequency mode, the dominant mode, is a certain number of cycles per unit length along the guide. The frequency is always the same, but the spatial arrangement can be different. A mode is a way of existing or travelling. If the wave travels with a differential spatial arrangement then the mode is different.

You have to "launch" microwaves into a guide. This ‘excites’ a particular mode in the waveguide. At the other end the receiving device will be expecting the same mode. If the mode changes (due to discontinuities or irregularities in the guide), other modes can be produced. These other modes will not be received efficiently resulting in power loss.

In physics classes the different modes of vibrations on strings are shown as different frequencies and different standing wave patterns. In the case of waveguides it is the pitch between maxima that changes. Look up:

mode, TE00, TE01, TM00, TM01, etc in microwave text books or on the internet.

From the electromagnetic compatibility (EMC) and interference (EMI) perspective you have common mode and differential mode.    

Differential mode is the easiest to understand if you think of a signal and a return path.  As these two nodes ideally carry the same current in opposite directions the sum (or difference) of the emissions generated by the current cancel each other out so ideally you have very little differential emissions (except maybe the magnetic field generated from the loop that the two paths form).  When things get non-ideal you'll get differential-mode emissions (all - forgive me if I'm describing this from a common-mode mindset).  

A common mode emission happens when a 'signal' is common to the signal path and the return path.  The actual return path for this common mode 'signal' is actually elsewhere in the circuit (capacitively coupling to GND maybe).  Think of a transmitting antenna - the power goes in but doesn't come out; that's a form of a common-mode emission.  Most EMC problems are caused by common-mode emissions, such as when a GND loop turns differential-mode signals into common-mode signals.  

Kimmel & Gerke did a great write up on this in about 1991 with EDN magazine.  It is out of print now but I read that they just released a new book (http://www.emiguru.com/).  They give a much more detailed explanation that this.  

In waveguides, I like to think of the "mode" as the "path which the electrons follow to get from point A to point B".
I can see an electron moving in my mind.  The path isn't always simple and straight.
kch

Of course the same mode would occur in a vacuum, so the presence or absence of electrons is somewhat arbitrary, especially since the gas in a waveguide is seldom ionised.