You cannot install Calendar Browser directly in the Office 365 Outlook. Instead you have to create a shared mailbox or public folder in Office 365 Exchange and then use with Calendar Browser.
When the shared mailbox is ready for use, each Calendar Browser user needs to add the shared mailbox to his/her local Outlook. This might be done automatically, but if not, the Tips article also describes how to add the shared mailbox manually.
Install and configure Calendar Browser in your desktop Outlook as described in the Calendar Browser manual and demonstrations
Select the Office 365 Exchange shared mailbox or public folder in your local Outlook when it is time to select Outlook folder.
Now all users who have access to the shared mailbox/public folder can reach Calendar Browser and book resources.
The shared mailbox solution is most suited for a smaller team, or when only a limited group should have the right to book resources. For a bigger group a shared mailbox will take too much time to handle, as each user has to get permissions on the shared mailbox and on the calendars.
For bigger groups we instead recommend installation in a public folder.
Another option for Office 365 is OWA (Outlook Web App), but OWA does not give the full Calendar Browser functionality.