Putting this shortly, we go through and we get launched into a blackhole.
How a mass effect relay works is by pretty much turning the ship to a very small mass, and it grabs you and slingshots you pretty much however far you need to go.
wait no, mass relays function by creating a virtually mass-free "corridor" of space-time between each other. This can propel a starship across enormous distances that would take centuries to traverse, even at FTL speeds.