What's actually happening
Every drain in your house eventually dumps into one pipe: the main sewer line. It runs from under your foundation out to the city sewer or your septic tank.
When several downstairs fixtures back up at the same time, the blockage is in that shared main, not in any single drain. That's why plunging one toilet does nothing.
The downstairs drains flood first because they sit lowest. Water always finds the lowest exit, and right now that exit is your basement floor drain or first-floor toilet.
Here's the quick confirmation test: flush an upstairs toilet or run an upstairs sink, then watch a downstairs tub or floor drain. If it gurgles or the water level rises, your main is blocked. No question.
This is an emergency because the problem doesn't hold steady. Every gallon of water you use has nowhere to go and pushes the backup higher.
What's causing the blockage
The cause depends heavily on your home's age and pipe material. Let me walk you through what I actually find on these calls.
In homes older than 40 years, tree roots lead the pack. Clay pipe joints leak just enough moisture to attract roots, which grow in through the joint and form a mesh. That mesh catches everything.
In any home, grease is the runner-up. Kitchen fat cools, hardens, and coats the pipe over years until the opening is the size of a pencil. One heavy day of use finishes the job.
So-called flushable wipes are a growing problem. They don't break down like toilet paper, and they snag on roots or rough joints and build a dam.
Less common but more serious: a bellied pipe (a sag where water pools) or a full collapse. Cast iron rusts through, and Orangeburg pipe from the 1950s just deteriorates into pulp.
The only way to know for sure which one you've got is a camera inspection after clearing. Anyone who tells you the cause without looking is guessing.