Project Online or Project Server 2013

Project Online is a new entry to Office 365 few months ago and is very effective as it provides the complete set of functionalities of Project server 2013 without putting any effort / money to buy
infrastructure for servers, software i.e. if you have to setup a Project server 2013 on your premises. you require  Windows Server 2012 / 2008 R2 SP1  , SQL server 2012 / 2008 R2 SP1 , SharePoint Server 2013 
Enterprise edition and for supporting all these you need a good supportive hardware with minimum 24/ 32 GB RAM , 80 GB minimum hard disk but for production you definitely require 160 GB at least  and then an
administrator who knows SQL , SharePoint and project server  beside basic networking , backup restore and Windows AD , then electricity cost / maintenance and  operational cost to keep the server online / available all the time
and lots of maintenance botherations/ tensions / performance monitoring etc.. Etc. All these are good / manageable for a large enterprise with more than 500 or 10000 users but for most of the mid segment and small organizations.
Project Online is the best solution which relieves you from any of the above mentioned costs and efforts and just you need is a good/stable internet connection which is commonly available now a days.

Compare feature availability across Project Portfolio Management offers

https://technet.microsoft.com/en-us/library/jj819260.aspx

To start with project online : Follow the links Below:

Step 1: Sign up for Project Online

Step 2: Get started with Project Web App

Step 3: Get started with Project Pro for Office 365

Step 4: Explore more features of Project Online