It's been hard to find a clear answer to this in the media. The most common surmise I've seen is that the new variant reproduces more in the nose and throat, and so people expel more of it when they sneeze or cough. But a recent NYT article suggests these as possible explanations:
In a typical coronavirus, the tip of the spike protein is like an ill-fitting puzzle piece. It can latch onto human cells, but the fit is so loose that the virus often falls away and fails to infect the cell.
The N501Y mutation seems to refine the shape of the puzzle piece, allowing a tighter fit and increasing the chance of a successful infection....
One mysterious [additional] mutation in the B.1.1.7 lineage [of the coronavirus] deletes the 69th and 70th amino acids in the spike protein. Experiments have shown that this deletion enables the coronavirus to infect cells more successfully. It’s possible that it changes the shape of the spike protein in a way that makes it harder for antibodies to attach.
I'd be curious to know what other accounts of the mechanism readers have seen. I'll conclude with observations by longtime reader Dr. David Ozonoff from the Boston University School of Public Health, with whom I've corresponded a bit about this:
I don’t think we know how (or truthfully even whether) the virus is more transmissible. Transmission is very complicated and depends on characteristics of the host (us), the environment (social behavior, season, etc.) and the virus itself. The evidence so far available does suggest increased transmission is very plausible but I don’t believe the evidence is ironclad (but it doesn’t have to be). In this context the exact mechanism (which is what you seem to be seeking) is just speculative and increased viral load is a reasonable speculation. Increased affinity for the ACE-2 receptor and increased infectivity of younger age groups has also been mentioned. I don’t think we can say what the exact mechansm or mechanisms is/are at work here.
UPDATE: Dr. Ozonoff just sent along this informative new article from the generally excellent STAT.