Stroke energy is the amount of energy you output on each pedal stroke, and depends on both your cadence and current power. It is proportional to torque (the base measurement of probably all power meters), but you may find its meaning a bit more relatable to what your legs are actually doing.
On a long ride it is important to avoid early efforts (when you're feeling strong and fresh) so that you aren't fatigued in the later stages. You could keep your power down, but your cadence might be too low. By monitoring stroke energy you can keep your effort down to a reasonable level without having to keep cross-referencing power and cadence. You can also maintain a tolerable stroke energy during specific efforts (eg, a hill climb) to avoid that dreaded burn-out in the legs.
Stroke energy is now available as a data field on Garmin devices, so you can add it to your regular screens. There are two data fields available in the Connect IQ store: real-time stroke energy and average stroke energy.