Say there's a quantum bowl with two identical red balls, and one blue ball. You take a ball with your eyes closed. Probably your ball is red, maybe it's blue. You open your eyes, see a color - what happened!
Here's three choices, none of them good:
1. Local Hidden Variables: When you open your eyes, you see which color your ball had all along! This is so obvious, but it's wrong for tricky reasons (Bell's Theorem) which I can't fit into the analogy; basically the ball cannot have "had a color all along."
2. Copenhagen: When you open your eyes, the ball just decides what color it is. The other balls will mysteriously agree, so there's not two blue or three red or whatever. How did they do that? Is that a real physical change, or just learning something new? (This is wavefunction collapse and it's very uncomfortable for obvious reasons.)
3. MWI: When you open your eyes, one version of you sees a red ball, and one version of you sees blue. Ok, but if there's red you and blue you, how can the red ball be "more probable?" Are there two separate "red ball" yous? Or maybe the red ball you is "more real?" (This is the relationship between the measure of the wavefunction and experimental probability, aka Born's Rule; MWI struggles to explain it, Copenhagen just postulates it).