Hypothetical example:
Let's say we have simplified market where we have 1000 bears and 1000 bulls traded every day and each bull/bear may trade 1 share per day. We will have 700-1000 shares traded every day in average. When we have more bears engaged in trading price is pushed down and when we have more bulls price is pushed up.
Now, let's imagine that at some point of time 500 bears turned into Bulls. Now we have 1500 bulls and 500 bears and daily volume cannot go above 500 shares per day because each trader has capacity to buy/sell only 1 share. We have drop in volume, we have dominance of the bulls and luck of the Bears and price go strongly up - Law of supply/demand.
This is very simplified, but it should give you idea how price can go strongly up on declining volume. Nice article about it:
http://www.marketvolume.com/advance_decline/overbought_oversold.asp