Strength is a military attribute and with rank it is very important for battles. More strength gives citizens more damage in battles. Check Damage Formula. The citizen's strength increases every time the citizens train.
Citizens can see their current strength on profile page. 
Once a citizen advance 5 strength points, he/she will receive Super Soldier medal and 5 gold 
for the reward.
Next Super Soldier medal and 5 gold will be awarded for every strength point the citizen gained afterward.