Unfortunately, there's a lot about Hummingbird we don't know right now. I think Danny Sullivan's FAQ piece is the closest we have to reliable information, but that still leaves a lot of holes:
FAQ: All About The New Google “Hummingbird” Algorithm
Google claims that Hummingbird is a substantial rewrite of the core algorithm (more than just your typical update), and yet we haven't seen large-scale movements on many client rankings. So, what's going on? A couple of things, I think:
(1) As Peter said (and this seems to be pretty well confirmed), Hummingbird changes how Google interprets some queries, especially natural language queries, and attempts to find relevant results based on a more complex, semantic analysis of phrases, and not just keyword matching. It's unclear how this practically impacts your average query today (especially head terms and the "chunky middle"), but as voice-based searches become more common and people get used to natural language queries, the impact will increase over time.
(2) Hummingbird seems to have increased Google's ability to use historical information to personalize queries. This extends a long-term evolution and means that any given person might see a different result for an ambiguous query based on previous queries. Even now, searches like "weather" bring up local information, whereas they used to bring up generic information (like weather sites). Practically, we're not seeing this personalization impact affect a ton of queries yet, but we will over time. There are ways to check ranking using context and limited personalization, but it's technically very difficult. This is certainly a concern for rank-tracking tools, including ours (and something we're thinking about even now).
(3) Finally, I suspect Hummingbird laid the groundwork for an expansion of Knowledge Graph, not only in its pairing to more queries, but in how Google extracts data from the index to create answers. I'm seeing many examples in testing where Google is pulling answer-like information from websites beyond its current data partners. This is speculation, and it may not be connected to Hummingbird, but these changes are definitely coming.
(1) and (2) impact rank-tracking directly, whereas (3) impacts how we view ranking and signals the need to go beyond just counting blue links. We take both trends seriously, but getting from here to there is a gradual process, not just for technical reasons, but because our mindset as SEOs has to evolve.
From a competitive standpoint, you won't see huge changes in the short term. If a change impacts any given query, that impact is felt for both you and your competitors, in most cases. There may be isolated examples where a re-interpretation of a query means that you or your competitor rise or fall in ranking relative to the other, but our tools would see that and I expect that's a relatively small amount of searches right now. At this point, we're keeping our eyes open and trying to predict where Google is headed. Now that Moz Analytics is launched, we're working hard to be more agile and iterate new functions in smaller chunks and at a faster pace.