"Assets" are an internal iOS mechanism to download data on demand. It's not available for third-party apps; it's only used by Apple. mobileassetd is the daemon in charge of managing and downloading assets when other apps ask for them.

The main example of assets is dictionaries (as in, for the user to see word definitions). Looking at the directory where downloaded assets are stored, it seems there's also fonts, the timezone database, firmware for accessories (like the Lightning to HDMI adapter), voice recognition data for the Hey Siri feature, etc. Even OTA updates of the iOS firmware are assets.

This has nothing to do with the "asset catalogs" feature you see when developing third-party iOS applications.