A fascinating paper by Lee and Swaminathan hypothesized a "momentum life cycle" for stocks that describes how share price and trading volume are interrelated. This paper has motivated subsequent research that illustrates how price momentum and earnings momentum are related. It does appear that trading volume plays an important role in determining returns. My personal take on this is that volume reflects the money flows of large, institutional traders who ultimately move markets.
I also suspect that it's not just volume in absolute terms, but relative volume that helps to determine returns. That would fit with the momentum life cycle notion, in which low volume winning stocks turn into high volume winners prior to becoming high volume losers (think: Internet stocks), low volume losers, then low volume winners. What is important is whether sectors or markets are attracting fresh capital as they move higher.
Eventually the high volume winning sectors attract so many momentum participants that performance stumbles (due to earnings disappointment, shifts in fundamentals) set off waves of selling and turn the groups into high volume losers. The sweet spot of portfolio selection is to catch groups that are low volume winners before they attract the momentum players.
Another personal speculation is that bull markets don't end until the high volume winners turn over. One "tell" that the August decline was not the harbinger of a freefall was that many of the winning groups (energy, emerging markets) continued to outperform the broad market.
An earlier post of mine discussed my efforts to measure "Technical Strength" by measuring the consistency of trending behavior. The momentum life cycle work suggests that an even more valuable metric would capture price change as a function of relative trading volume.