Update: According to Verizon, the Jelly Bean rollout for the RAZR HD and MAXX HD will begin next week.

The Verizon support site has been updated with Android 4.1 update docs for the RAZR HD (and the MAXX HD).

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The update rollout process should follow soon, in the next week or two. The Android 4.1 update brings, as you well know by now, expandable notifications, Google Now, and a variety of tweaks like Project Butter, to make your phone run smoother than ever. The update version is 9.1.41.XT926, so be on the lookout.

Non-Jelly Bean related changes include the removal of some older Verizon bloatware apps, and the addition of the new Amazon Suite that now comes standard on all Verizon Android phones. The requisite "improved voice and data connectivity" is also in tow, and the native Motorola calendar app has seen improvements as well.

Verizon Support [1] [2]