Morale
Morale is an aspect of your dominion which affects your OP and DP. In some cases it can affect your Prestige gains from attacking. It is reduced by exploration and invading.
Drop
Invading causes an immediate drop of 5% for attacks 75% and greater of your land size. For hits below 75%, the following formula is used as well:
((Range - 0.40) * 100 / 7) - 5
You cannot invade if your morale is below 70%.
Exploring is not limited by morale.
Effect
Morale is a multiplicative bonus.
Bonus * Morale Penalty
The Morale Penalty is calculated as 0.9 + (Morale / 1000) where morale is between 70 and 100 inclusive
Morale affects Prestige gains differently than above, which can be found in the Prestige page.
Refresh
Morale refreshes by 6% per hour when under 80% and by 3% when 80% or higher.