Non-platform-specific changes for the Steam Linux client includes updates to the desktop user interface styles, a major updated to the embedded web browser, and various fixes. The embedded browser update betters the performance and reliability along with having other security and functionality updates. There's also an assortment of other Big Picture mode enhancements and fixes.
Linux specific changes with this latest client update include the Steam Runtime supporting newer compilers, support for entering custom network settings within the Big Picture mode, fixed audio when alt-tabbing, a crash fix during voice chats, and a fix for launching SteamVR games.
Steam Linux gamers wishing to learn more can read the lengthy change-log found at SteamPowered.com.