Short answer: Yes, with an "and!"
Without getting into too much engineering or discussing the Bernoulli principle, yes, exhaust back pressure is a thing, and while you’re probably not going to care too much about the what, you’re going to want to know about the why.
I am going to stick with four-stroke systems, since while two-stroke systems have extremely interesting exhausts for very specific reasons, most street motorcycles are four-strokers and that is our readers’ majority concern. (If you’re interested, look up some two-stroke exhaust designs and the engineering behind them, because it’s pretty fascinating.)
Your Bike's Exhaust Isn't Just a Tube
The most important things to know about your stock motorcycle exhaust are that it was designed by a bunch of really smart engineers at the factory where your motorcycle was created, and it is not just a hollow tube. There are all kinds of things going on inside there: the internal shape of the pipe combined with the initial header length, points of expansion and internal routing (sometimes there are pipes in your pipes) all work together to keep the waves of exhaust gases produced working for your engine and not against it.
What's Actually Happening
The exhaust gases that exit your engine do not do so in a smooth flow. The four-stroke “suck, squeeze, bang, blow” operation dictates that exhaust gases pulse into the pipes on the “blow” step. That pulsation can result in back pressure.
The shape of your exhaust system works very precisely with these exhaust pulses to maintain rearward flow: all of the gases flow toward the exit instead of back up through the exhaust port and into the engine. A well-designed exhaust will use the precisely-timed pulses to create a similarly precisely-timed vacuum. This effectively not only pulls the spent fuel out of your cylinder in preparation for the next “suck” step but, at peak power RPMs, helps the next round of air and fuel begin to enter the cylinder even before the piston itself creates that vacuum. This helps engine performance, and helps keep your power band nice and wide and usable.
Design Is Important
If you replace your exhaust system with one that was not designed for your bike (or, in some cases, not “designed” at all unless you want to count a welder and some plumbing parts a design), you’ll experience an increase in noise, an increase in unburnt fuel coming out the back of your bike, and a decrease in torque, usable powerband, and overall performance. All that precise timing goes away. That “back pressure” you may or may not believe in can, in fact, push gases back into the cylinder. Instead of exiting rearward, the back pressure exhaust gases tumble forward, diluting the fresh air/fuel mixture, and sending your bike’s performance into the toilet. Flat spot much? The bike may run great at some RPMs and terrible at others: this is often a sign of a poorly-tuned exhaust with too much back pressure.
Have You Had A Leak?
If you've ever experienced a leak in your exhaust system due to something like a failed header gasket or a rust hole, you know first hand the absolute chaos that introduces. Your bike suddenly runs like crap! That's because all that engineering that keeps your bike running and your exhaust gases flowing in a beautiful symbiotic dance has gone directly out the window. No amount of tweaking your carburetors or remapping your EFI can help; exhaust leaks mean the gases are not exiting cleanly and your bike can breathe in but it can't breathe out. Back pressure is literally choking your bike.