The problem with bags is that the knot is dense and hard while every other part of the bag is soft and weak. What you're going to do is twist the end so that it becomes dense. The other advantage is that when twisted, it will get a lot narrower, allowing it to slide through the hole of the knot. It will actually be dense/strong enough that you will be able to push it through the hole. See the video for an example. Again:
1) Twist bag near the knot until it's hard.
2) Push the end through until the knot is completely loose.
3) Pull out knot.
4) Brace yourself against the crowd of adoring fans who now think you're a superbeing.
For an explanationg from a simplified engineering perspective, it goes like this. Some materials are stronger one way than another. For example, paper. Paper has excellent tensile (pulling) strength but terrible compressive (pushing) and shear (think ripping it in half) strength. Take a of computer paper and try to pull it apart (no tearing). It's really hard. Now try smushing or tearing it. really easy, right. The same is true about the bag. However, many materials can have these properties changed by changing the shape. If you roll that piece of paper into a tube, it becomes a lot harder to squeeze it. The same enhancement makes the black magic you just did with the bag possible. In my Design and Manufacture class, the professor bought in a board of wood to explain grain. When the force is "against" the grain, the wood is strong, and he was able to stand on the board suspended between two supports. When it is "along" the grain, the wood is weak, and the professor (not exactly a body-builder) was able to easily break it by chopping down with his hand.
This should give you a basic understanding of whats happening. Also, my professors are awesome.
When closing the bag, grab the bag loosely by the end and flare out the very end over your hands. Now breath out and breath in from the bag. This will suck out extra air and keep the contents fresher.
When tying the knot, avoid this problem by tying a slip knot. You may have conquered the knot, but lesser people have not.