To start, let's talk about what it means to lug your engine. This is the term used to describe when you're puttering along in a higher gear than you need to be in and the engine is turning low RPMs. When you're cruising along in 6th but you should've downshifted into 4th about a half mile back, you are lugging your engine. Why is this bad? Engineering Explained is here to lay it out for you.
When you lug your engine, you are forcing it to work far harder than it should. Low RPMs are fine if you're just cruising or slowing down, but when you accelerate, low revs leave your engine with a gearing disadvantage.
To get your car up to speed, the engine has to work a lot harder. Engine temperature will rise, and cylinder temperature will rise. This is where things can start to go screwy.
Picture yourself on your old 10-speed road bike. You're cruising along, having shifted up into the higher gears. Suddenly you need to accelerate and when you try to turn those pedals, you find it takes a lot more effort than it would if you were in a lower gear. You are working far harder than necessary just to get that bike moving again.
In this example, you've lugged your body because you're the engine of the bike. It's not fun to do that, so why do it to your car? Plus, your engine makes more exciting noises when you're in the right gear during acceleration, especially if it's a V-8.