A city with a high morale will be more productive. The Farm, Sawmill and Stonemason will produce quicker, troops will work harder when attacking or defending, Research and Crafting times will be reduced. A city with low morale does the opposite to all those things!

Tapping on the population tab in your City will show what is helping or hurting your morale so you can do your best to maximize it. Build up your city, win battles, and grow your family to boost morale.
Keep in mind that you can only attack players that are the same Keep level or more than yours, if you attacked a player 2 levels or more below you, you will get penalized and will receive debuffs for your army. The lower the level, the stronger the morale penalty.

TIP: Make sure your housing is inside your walls, otherwise the people living there will feel vulnerable, which will hurt your overall morale.