This is the Power Bash ability under the Block section. The description in the game doesn't say that it needs a shield.
While not all of the perks in the Block skill apply to non-shielded blocks, the ones in the right branch (which contains Power Bash) apply to both shield and two-handed weapon blocks.
No, it doesn't work for two-handed weapons. I tried it and there is no difference to the normal bash, where as if you have a shield equipped there is a noticeable improvement. Kind of unfortunate, in my opinion.
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Some of these responses are not correct. I can both stagger and disarm using my power bash with a two hander. Additionally, the stamina use for a power bash is greater than that for a normal bash (comparing after use of each). – user17363 Dec 29 '11 at 22:53