An update to the remote desktop client was recently applied to my MacBook via the software updater. I can't find this application anywhere. What is this application called and where is it located?
To take advantage of the functionality you've just seen updated, you probably need "Apple Remote Desktop", which seems to be an enterprise remote management tool like Microsoft's Systems Management Server, but for OSX.
The update you're referring to probably updated unseen client-side support built into OS X. For desktops that aren't being managed by Apple Remote Desktop, I would guess the update is innocuous.
UPDATE: For what it's worth, I just ran Software Update on my own MacBook and saw the update you're referring to. Here's the link to Apple Support's article describing the update. In fact, it mentions:
[...] Apple Remote Desktop Client 3.3.1 updates the software that facilitates Remote Management (enabled in Sharing preferences, in System Preferences). [...]
Perhaps you’re referring to the Screen Sharing app. It’s in Macintosh HD > System > Library > CoreServices.
P.S. You don’t need to launch this app directly to connect to another computer via VNC. You can just go to Finder > Go > Connect to Server… (or press ⌘K) and enter vnc:// and the address of the remote computer. This app is also used by the Back To My Mac screen-sharing feature.
The update in specific updated the programs found at
/System/Library/CoreServices/RemoteManagement/ - specifically ARDAgent.app
ARDAgent goes hand in hand with Apple Remote Desktop which is used to help manage multiple Macs either through controlling (ala VNC), copying files, installing packages, restarting, etc. For most people it's a non-issue. For businesses or other places that use Apple Remote Desktop the new version brings some very nice bug fixes. (I'll never log myself out again trying to log off a remote computer again!)
Cross-post from AskDifferent for Googlers
If you are trying to access one of your own computers that uses your same Apple ID, the best method is to use Back to My Mac.
You have to make sure you enable "Back to My Mac" in the iCloud Preference Pane on both computers:
Under the Sharing Preferences pane disable Remote Management if it is enabled, and then enable Screen Sharing.
Wait a moment and your computer should show up in Finder under the Shared section.
If you don't see a "Shared" section or the computer doesn't appear there, click on Finder and then open Finder's preferences (⌘+,) and make sure that everything in the Shared section is selected: