this is a tough concept for many people to grasp...that's OK. i'll try to put it in layman's terms as best i can. the fact that the force of gravity changes with distance gives rise to the term "tidal" force. that is, tidal forces are really just differences in the force of gravity between one location and another. clearly the oceans facing the moon have a greater gravitational bond with the moon than the oceans on the side of the earth opposite the moon. while howstuffworks.com's explanation of the bulge on the opposite side of the earth isn't totally incorrect, IMO its a pretty poor explanation. the bottom line is that the moon pulls harder on everything closer to it (the oceans, the mountains, and the entire earth itself for that matter) than it pulls on anything that's farther away from it. that is, as you get progressively further away from the moon, so does its gravitational force on you get progressively weaker. hence the tidal force's ability to "stretch" things out along the axis of force (in this case, the force of gravity).
another example that helps alot in visualizing this concept is a body in the vicinity of a black hole, particularly a stellar mass black hole (as opposed to the super-massive black holes found at the centers of galaxies...but that's neither here nor there). black holes are known for their very disruptive tidal forces b/c their gravity is so strong. let us suppose you're falling toward a black hole feet first from very far away. you would not be able to notice the difference in the amount of gravity of the BH exerts at 10 billion miles out versus 9.9billion miles out for example. and yet during that time, you'll have fallen 100 million miles closer to the black hole - that's a long way to travel toward a massive object and not feel the change in gravitational force. but the closer you get to the BH, the greater its gravitational force becomes. eventually you'd get close enough to the BH to where the difference between the gravitation force pulling on your feet is significantly greater than the gravitational force pulling on your head. this is "tidal forces 101," and the closer you get to the BH, the greater the tidal forces become (and the greater the difference between the gravitational pull on your feet vs your head becomes). you will eventually get stretched out along the axis of force, and your feet will accelerate toward the BH at a greater rate than your head, stretching you out like a piece of spaghetti.
so that is why there is high tide on opposite sides of the earth at any given time. that is, the above explanation is why the earth (along with its oceans, since they are fluid) takes on an elongated shape along the axis of gravitational pull. i can see how some folks still might be cofused as to why all the oceans don't just flow to the side of the earth nearest the moon, but it just doesn't work that way. tidal forces have the tendency to stretch things out along the axis of force, giving matter farthest from the source of gravity the appearance that it is being stretched in the opposite direction, when really its getting pulled in the same direction as everything else - just less so b/c it is farther from the source of gravity.