Any kind of electrical power transfer has a typical ratio of voltage to current. For example, you can deliver 100 watts by 1 amp at 100 volts, or 10 amps at 10 volts, or any other product that comes to 100. It's convenient to express the ratio of volts to amps as a number of ohms (since dimensionally that's all ohms are anyway). Power sources, loads, and even transmission lines all have characteristic impedance, which tells you something about what will happen when things are connected together.
Impedance matching is the selection of components with identical impedance, or the addition of impedance transforming components to cause a component with an undesired impedance to appear as though it has a more desirable one.
As Brian Carlton pointed out, when you have matched impedance, you achieve maximal power transfer. This is often desirable, but not always. The thing to remember is that maximal power transfer is achieved at the cost of dissipating equal power in the source and the load.
So for example, a case for not matching impedance is when you want to efficiently use the energy from a source. A 0.1 ohm load would get optimal power out of a battery with a 0.1 ohm internal resistance, but half the energy would be dissipated in the battery itself, which would be rather wasteful of the stored energy. (Not to mention that the terminal voltage would fall to half!) By purposely using a load much with much higher resistance than the battery, most of the stored energy ends up doing work in the load.
On the other hand, you DO want to match impedance when, for example, you have an audio amplifier stage that ideally wants to drive a 600 ohm load, but you only have a 3.2 ohm speaker. An ordinary transformer, having a 1:N voltage ratio, will conveniently give you a 1:N^2 impedance ratio. Another common case is in RF work, where as volting pointed out, you need to minimize reflections, because reflected energy can cause excessive power dissipation in your source.
I think your confusion is shared by many after they first encounter the maximum power transfer theorem. In essence, many forget the question the theorem answers.
The question the theorem answers is: For a given source impedance, what load impedance results in maximum power transfer from source to load.
Unfortunately, I've seen trained engineers reverse the question and then try to apply the same theorem, i.e.: For a given load impedance, what source impedance results in maximum power transfer from source to load
Many who should know better will answer "match the source to the load". But that's just plain wrong. A zero source impedance delivers maximum power to any load because there is no power loss in the zero source impedance.
Best Answer
Make sure to use the best possible measuring methods with the scope to avoid the introduction of false impressions. Short GND lead referenced right at the load measure point.
Make sure the series resistor in the signal line is as close to the driver output as possible.
The series resistor value may have to be adjusted up or down to improve the line match.
For particularly critical applications you may need to place a pullup and pulldown on the very end of the line to match line impedance and prevent reflections. The match impedance is the parallel equivalent resistance of the two resistors.
If you have this all built on a proto plug board with flying wires everywhere the pictures of the waveforms may be as good as it gets.