This update contains bug fixes and security updates.
The support document referenced for additional details gives only two specific changes, the second of which is likely of interest mostly to enterprise users.
Fixes an issue that may prevent some Mac computers from waking from sleep when connected to certain 4K displays.
Third-party .pkg file receipts stored in /var/db/receipts are now retained when upgrading from OS X Yosemite.
For iOS 9.2.1, Apple says:
This update contains security updates and bug fixes including a fix for an issue that could prevent the completion of app installation when using an MDM server.
Again, that’s relevant chiefly for enterprise users.
The updates also address a handful of security vulnerabilities: nine in 10.11.3 and nine in iOS 9.2.1. As a reminder of how much code is shared between OS X and iOS, five of the vulnerabilities were the same on both operating systems.
You can install the OS X 10.11.3 update (661 MB on an iMac with 5K Retina display) via Software Update or from Apple’s Support Downloads page (662 MB for the delta updater from 10.11.2 or 1.47 GB for the combo updater from any version of 10.11). Install the iOS 9.2.1 update (37.7 MB on an iPhone 6) via Settings > General > Software Update, or through iTunes.
Unless the enterprise-related fixes are essential for your organization, we recommend holding off on these updates for a week or so. When Adam updated to 10.11.3, his iMac hung at a black screen with a Restarting progress bar two-thirds filled. It came back up properly — fully updated — after he powered it down, but on the off chance that his experience is indicative of a more general problem, delay the update for a bit and watch for reports from other users. When you do decide to update, make sure to make a backup first!