Refers to a running back's style of rushing the football where the ball is ran in a usually straight and direct manner through the defensive line, and has very little to do with actually running down a slope. A downhill rusher primarily runs the ball up the field with power towards the opponents endzone with the help of the offensive line as opposed to running out to the sides towards open field and using skill moves like zig zagging and juking to make the tacklers miss.
Downhill runners are known for their strength and toughness because once they are handed the football they usually run directly towards the defensive line and linebackers (like a bowling ball). It's the offensive line's job to open up gaps so a downhill runner can penetrate into the linebackers and defensive backs for a big gain.
Jerome Bettis is a classic example of a downhill runner. Barry Sanders would not be an example of a downhill running back since he was known more for shifty runs and making the defensive players miss.