Starting on January 1 2019, Steam will officially stop supporting macOS versions 10.7 ("Lion"), 10.8 ("Mountain Lion"), 10.9 ("Mavericks") and 10.10 ("Yosemite"). This means that after that date the Steam Client will no longer run on those versions of macOS. In order to continue running Steam and any games or other products purchased through Steam, users will need to update to a more recent version of macOS.
The newest features in Steam rely on an embedded version of Google Chrome, which no longer functions on older versions of macOS. In addition, future versions of Steam will require macOS feature and security updates only present in macOS 10.11 ("El Capitan") and above.
For the remainder of 2018 Steam will continue to run and to launch games on these versions, but other functionality in Steam will be somewhat limited. For example, new features such as the new Steam Chat will not be available. We encourage all users on these operating systems to upgrade to newer versions of macOS in order to have ongoing access to the latest features of Steam, and to ensure future access to all games and other Steam content.
Users of macOS versions 10.7 ("Lion") through 10.10 ("Yosemite") can find more information on upgrading macOS here.