A mailbox is placed on Litigation Hold in case the person is subject to Investigation. Once the mailbox is placed on Litigation Hold, the person would not be able to delete emails from his account. The quota for the recoverable items in a folder increases from 30 GB to 100 GB. The reason for this Increase is that the mailbox should be capable to hold all emails which includes deleted emails.
In order to enable this functionality one needs to be an Exchange Administrator. One would basically need to go onto Exchange Online Administration. And click on Recipients. Then activate the Mailbox tab. Search for the Mailbox you want to put on Litigation Hold and select it. The click on the pencil icon in order to edit the properties. This opens up a new window. Now click on Mailbox Features and under Litigation press Enable. This would take you to another window. Here you can specify the duration that the Mailbox would be put on Litigation Hold. In case it is indefinite leave that field blank. And click Save, this would now enable Litigation Hold on the Mailbox. It would take approximately 60 minutes for it to be fully enabled.