In phase situations tend to reinforce each other, out of phase situations tend to inhibit, or cancel the effects of each other. When you tune your radio to a certain station, you are changing the characteristics of your receiving device so that it is in phase with the transmitter of the station.
In phase is a powerful thing; in airplanes, for example care must be taken to ascertain that the skin is never in phase with the vibrations of engines or airflow so that it does not fatigue and rip apart :)
In Elecrical theory the significance of a phase ( meaning the time relation between two quantities volts to volts or volts to current ) directly implies that there are components present whos action is frequency dependant .
Such as capacitors inductors transformers .
Phase is a time relation between two repetitive waveforms ( the simplest being sinusoidal ) of the SAME frequency , but is measured in degrees .
360 degrees is equivalent to one complete signal repeat period.
For signals to be 'out of phase ' usually means that there is a 180 degree shift of one of them.
However this does NOT imply they cancel -- since to do this they must have an identical shape in time and be of equal magnitude.
A simple capacitor will yield a 90 degree shift between it's current and voltage waveforms ( sinusoidal ).
However an Audio amplifier will generally exhibit a phse shift between it's input and output voltages at a few kHz, Due to the presence of capacity
inherent in some components or placed there for stability reasons.
Phase, when considering a single waveform has no significance. Only the difference in phase between two waveforms has significance. Phase difference determines what the outcome is when you add two waveforms together. For example, adding two sine waves (equal in amplitude and frequency) in phase gives you a second sine wave with double the amplitude, adding two sine waves 180 degrees out of phase gives you no signal (zero for all time).
Including phase information is a prime motivation for using complex numbers to mathematically represent oscillatory phenomena.