For the OP, the simple way to think of this is the lower the impedance of the "load" in this case the bass cabinet (the 4 ohm vs. the 8 ohm), the easier it is for the amplifier to send more current to the speaker. Some amps are designed to handle varying "loads" - but you always want to err on the side of caution. As a post above mentioned, if the amp in question wasn't designed to handle the increased current output, you could "fry" it - meaning that any number / type of components could fail if they aren't designed to handle the higher current output.
Just remember that the lower the impedance of the cabinet, the less resistance there is for current flow. You'll also frequently see that some amps will give a power rating for 8 ohm loads and a higher power rating for 4 ohm (or less) loads. That's the principal we're talking about in action. A simple example would be an amp that is rated at 350 watts into an 8 ohm load, and 500 watts into a 4 ohm load. Very common these days on newer amp designs. In those cases, the internal components are spec'ed to handle the higher current.