What is Frequency in electronics?
Frequency, in the generic sense, is the rate at which something repeats.  Usually measured in "repetitions per second", or Hertz (Hz).  My watch ticks at 1 Hz.  I water my lawn at a rate of 0.00000386 Hz. And my car blinkers blink at about 0.5 Hz.  That's it!  Of course things get a little more complex when you consider what exactly is repeating.  But "frequency" really is that simple.

A scope, or band pass filter, is usually rated in Hz and refers to the frequency of a signal that can (or can't) go through it.  In this context, it is talking about a sine wave.

Something like a 555, or other clock signal type circuit, is talking about how often the signal switches.  

The term "DC" is often abused, so don't take it too seriously.  Most of the time it refers to a power supply that outputs a steady voltage.  But it could also refer to anything that outputs a signal that is only a positive voltage.  Or, it could refer to a signal that is a "mostly constant" voltage.  But, if the signal is truly unchanging then it has a frequency of zero.  

Bandwidth and frequency do have a relationship-- in much the way that a car and a baseball are related (they are both measured in miles per hour).