This is a somewhat advanced topic, with a multiplicity of points of view and formulae to back that up.
I think the following photo.net article comes close to explaining it well:
http://www.photo.net/learn/optics/dofdigital/
The article summarizes, within certain condidtions (see article), as follows:
Depth of field is proporitional to (circle of confusion) / (focal length) ^ 2
The two factors work against each other in smaller frame cameras -- circle of confusion gets smaller (thus implying lower DoF), but focal length gets smaller, and the division and square factor magnify its effect. This "explains" how digicams get their greater DoF -- because, to get the same field of view in a small sensor, you need to have a smaller actual focal length.
Other explanations emphasize the effective diameter of the lens. But this is focal length / f-stop, so the focal length is an implicit player here.
Yet other explanations imply that focal length makes no difference, but they do this by changing the subject distance greatly. Therefore focal length does matter, because if it didn't, why would they have to change subject distance? Subject distance matters greatly too.
Essentially, subject distance, focal length, aperture, and circle of confusion all matter, and make the topic difficult to grasp. When we factor out aperture and subject distance to compare different format sizes, the smaller circle of confusion penalizes smaller format size, but the smaller focal length for the same field of view turns it around, giving smaller formats greater depth of field.