Systematic HR has an excellent post on HR strategy, both what it is and what it isn't. While the piece will likely ruffle a few feathers, I think it is interesting to look at the gaps in perception between HR and the business as a whole.
What it basically comes down to is your focus on the business. Each and every task performed should be with your executive team’s strategic business plan in mind. In other words, HR is not strategic when it is not coordinated with the business strategy.
While the above summary is reasonably well understood (or should that be that its been written many times in different forms?!) I still think there is scope to narrow the gap between HR and the business, where such a gap exists. Personally, I think that the use of Christensen's Values, Processes and Resources, or VPR (diagram here) view of the firm offers people the simplest and most comprehensive means to understand, act on and close the HR/Business gap.
In brief, I think HR has a great claim to two of the three aspects of the above, namely Values and Resources. Talk of culture, missions and values can be owned or significantly influenced by HR. Likewise, Resources is only one removed from Human Resources! This leaves Process and aside from HR processes, having an understanding and making a contribution to this from a HR standpoint is a distinct possibility.
N.B. despite my own enthusiasm for the VPR framework, this page from Google only returns two results!