Hangouts is the standalone app for Google's conversation hub, Hangout, and for the most part recreates the desktop experience very well, even adding some additional features for broadcasting on the go. The app, which is scaled for both iPhone and iPad, is designed for sharing content and is deeply integrated with Google+. If you enjoy using Google+, then this app is a natural extension of that.
Google's Hangouts is already a very popular and efficient tool, offering a free alternative to pricey Web conferencing tools. However, the mobile app takes that functionality to the next level. The Google designed interface is of course attractive and easy to use, but beyond that, Hangouts connects with all other types of accounts, even other computers, and you can pause and continue your hangout between devices. You can also send photos or text messages from your device with the app, something other video chat tools don't always support. There are issues, of course. Inability to see who is online, inability to set your status when logged in as you would in Skype, and the requirement that you have an active Google+ account are all issues that can limit usability for many potential users.
Google's Hangouts app is a fine extension of their Google+ service. It is not for everyone, though, namely because of its social-based restrictions. If you use Google+, however, and want a free Web video chat tool you can take with you on the go, Hangouts is a great option.