This command costs only one TP and gives a random number of morale to the selected soldier, you receive more morale if your Officer is experienced. It is highly effective when your officer is at 30+ exp, and Officers with 80+ exp can give boosts of 50+ morale to certain troops. When you have multiple officers on the field, the one with the highest experience will give the morale boost. Your Officer can also give morale boosts to himself. Once a soldier gets over 100 morale, they cannot be boosted any more, instead it tells you that 'This soldier is fine for now, thanks' and you don't lose any TP. If you deploy Frenchies often, use this as soon as the Frenchie is deployed to keep him from running away.
Snipers are not very affected by morale boosts.
Depending on the circumstances, your Officer CAN stop an allied unit from running away with morale boost (as long as it bumps morale back above 0).
Before patch 2.2.5 if you gave a grunt a morale boost you could keep clicking any other grunt and it would still raise their morale (that's why you would commonly see multiple soldiers back then with 100+ morale).
The voice clip that plays when you use the morale boost on a troop is from the game Medal of Honor: Allied Assault in the D-Day mission.