Why does electricity have a phase?
Phase is a difference in time between signals that have the same frequency. 

Here is a picture of three sine waves:



If you looked at one of A, B, or C at a time without a well-defined starting point, you couldn't tell the difference between them. The only reason why they're different is because they get back to their 'starting point' at different times.

This isn't exclusive to sine waves - you can talk about phase for any periodic signal. Note, however, that every periodic signal is a sum of sine waves, so you're really just talking about the phase of the fundamental.