The new macOS Catalina beta can be downloaded using the Software Update mechanism in System Preferences after installing the proper software from the Developer Center.
We don't yet know what improvements the third update to macOS Catalina will bring, but it will likely focus on performance improvements, security updates, and fixes for bugs that weren't able to be fixed in the macOS Catalina 10.15.2 update.
macOS Catalina 10.15.3 has code in it that suggests a new "Pro Mode" is coming to Apple's Macs. Pro Mode appears to be an optional setting that overrides fan speed limits and energy saving restrictions to improve performance. The code says that apps "may run faster" but battery life could decrease and fan noise could increase.
It's not entirely clear if Pro Mode is coming to Macs in the 10.15.3 release, but the code is there so it is a possibility.
We didn't find any other new changes in the first beta of macOS Catalina 10.15.3, but we'll update this post if there's anything new in the second beta.