So far this thread doesn't have electrical misinformation in it. It will soon. I like homes' explanation. I is current. R is resistance. Someone will eventually point out that a speaker isn't a purely resistive load but his explanation is a good way to look at it. if you halve the resistance (R) you will approximately double the current (I). In my first physics class I asked why C wasn't used for Current and never got a good answer. i have a physics degree from the University of Chicago. So we will keep using I for current.
I'll add one more thing: many good amps will provide double the power to a 4 ohm speaker as it is rated for an 8 ohm speaker. but some can't. That is generally a current (amps) limitation.
Jerry