A Chrome for iOS update in April introduced pull-down gestures that made it easy to open a new tab or close the current tab when browsing on your iPhone. That was, however, the extent of Chrome's gestures for the iPhone. Chrome still forced you to tap the forward- and back-arrow buttons to navigate pages while Safari let you swipe to navigate forward and backward.
With an update yesterday, Chrome now supports swipe gestures on the iPhone to navigate forward and backward. Specifically, swipe right to go back a page and swipe left to go forward. The arrow buttons still remain in the upper-left corner, so you can continue to tap them if you are so inclined. But if Chrome auto-updated and you missed the introduction of the newest gestures, you can do less tapping and more swiping if that's how you'd like to navigate Chrome on your iPhone.