An abstract noun is a noun that you cannot sense, it is the name we give to an emotion, ideal or idea. They have no physical existence, you can't see, hear, touch, smell or taste them, but you can experience them. The opposite of an abstract noun is a concrete noun.

For example:-

Justice, an idea, bravery, and happiness are all abstract nouns.

Here is an a-z list of some of the more common abstract nouns:-

adoration artistry        
belief bravery        
calm charity childhood comfort compassion  
failure faith feelings friendship    
happiness hate honesty hope    
idea impression infatuation      
law liberty love loyalty    
maturity memory        
peace pride principle power    
redemption romance        
sadness sensitivity skill sleep success sympathy
talent thrill truth      

See also Concrete Nouns

Thanks to DP for the correction.