Chrome 57 will throttle background tabs to save power according to some information on this latest release over at the Chromium Blog. This change will apply to both Chrome 57 on the desktop as well as Chrome 57 on Android devices, so no matter where you use Chrome to do the most web browsing, post update you should notice Chrome eating up less power than before. Having said that the Chrome team does note that it's on the desktop where Chrome uses up a third of the overall power usage that comes from Chrome, so the power saving benefits of the background tab throttling might be more apparent for desktop users than mobile users, although there is no indication that it won't be equal.
In Chrome 57, if the browser notices that background tabs are using a large amount of power, it will limit the timer fire rate for those particular tabs, and this apparently leads to a 25% decrease in the number of busy background tabs, which in turn translates to less power consumed by Chrome and saves the user a little bit more battery life, which is definitely a good thing. How noticeable that will be for each individual user will depend on the user, and how they browse Chrome, for example, how many background tabs they tend to have open, but in general it should still save a little bit on power for all users.
While saving battery power is a good thing, Google also doesn't want their methods for lessening the power consumption to lessen the experience for users, which is why they've made it so that the new throttling mechanism won't affect any background tabs which have audio playing in the background or tabs which need a constant connection to continue working the way they're intended. The Chrome 57 update began rolling out to desktop users as of March 10th, so it should be live for most of if not all users at this point, and the same update should be hitting Android devices fairly soon as well if users don't already have the update. This follows the update to Chrome 56 on Android which all users should already be on, which started hitting devices back at the beginning of February.