The rubber compresses the veins making the part before the rubber expand a bit and become easier to see.
This makes it easier to poke the needle into the vein without missing and without going completely through the vein(not a good thing).
After the needle is in the rubber can be removed with little effect and often is.
There will be a slight reduction in flow.
Well, it's not so much that it compresses the vein, it's that it stops the flow (veins carry blood BACK to the heart), causing the vein to plump up. But yeah, what he said.