If you use a lower load, (=resistance, measured in ohms) than rated, the amplifier will be over-driven, causing it to over heat.
Just like opening a tap... by using 4 ohms instead of 8, you are increasing the "flow" (amperage) the amp has to produce.
Ohm's law dictates that by lowering the resistance, with the same voltage, you will increase the amperage. (current)
This also increases your watts. (volts x amps)
*EDIT*
Forgot to answer the first part of your question.
Yes, 4 ohms is lower than 8, but you ARE confused aren't you.
It's the opposite... it's the speaker's load (resistance) that the amp has to handle. A lower resistance means a higher demand.
You're confusing this with the wattage(power) the speaker can handle.
So to recap: The wattage is produced by the amp, the resistance is "produced" by the speaker.