Cloud Mining is simply using shared power from a different data source. Cloud Mining allows you to mine from home with very few requirements, which include a computer used for communication and a wallet to store your coins. With the ease of cloud mining comes certain challenges such as:

Exposure to fraud
Very little control and power
Less profit intake
Legal contracts which you may not entirely agree with

With that being said there are also several benefits which come with cloud mining including:
Peace and quiet at home (no fans constantly making noise)

No extra electricity costs
No equipment to sell if mining becomes less profitable
No need to cool your house with fans or air conditioning

You typically have 3 options when it comes to cloud mining, which are hosted mining, virtual hosted mining, and leased hashing power. Hosted mining allows you to lease mining equipment from the provider. Virtual hosted mining typically means you have created your own private server and installed your own software. Finally, leased hashing power allows you to lease a percentage of hashing power without your having to own a virtual or physical computer.