Hi Nick,
Signal Fundamentals
An energy signal has a finite energy. Signals of a limited length also carry a finite energy, and so they are energy signals. A signal that decays exponentially can be another example.
A power signal is not limited in time and has an infinite energy. Since an infinite energy has no meaning for us, then we use the energy per unit of time,which is power.
For example, if x(t) represents the potential (in volts) of an electrical signal propagating across a transmission line, then Z would represent the characteristic impedance (in ohms) of the transmission line. The units of measure for the signal energy E(s) would appear as volt2·seconds, which is not dimensionally correct for energy in the sense of the physical sciences. After dividing E(s) by Z, however, the dimensions of E would become volt2·seconds per ohm, which is equivalent to joules, the SI unit for energy as defined in the physical sciences. - (Wikipedia)
I hope this helps,
Kevin