I have no idea what that pipe might be for. I'm assuming there is another pipe where your washer machine water empties out into.

That doesn't look good. Maybe you should stuff it with a rag. You don't know if it is emitting sewer gases.

Yes, there is another pipe hooked up to the washing machine. I'll get a cap for it the next time I'm at Lowes or HD. It just seems strange I've never noticed a smell from here until now.

Don't cap it until you consult a plumber.

How does your dryer vent? Could it be a vent pipe? Agree with consulting a plumber.

This is an outside wall and there is a hose that goes from the dryer to the wall that's to the left and lower down on the wall from this one.

Ok, I guess I'll call a plumber. I hate to pay someone to come out and tell me I just need to cap it, but I also don't want to ignore something that could turn into a bigger problem if ignored.

Am I seeing a bit of a ridge running across the wall above it? Like the wall has been repaired? Are there any other signs or repairs or changes made in the area?

I can make some guesses, but I'd call an experienced plumber. You want the older guy who has seen the good, the bad and the ugly. in the meantime, you can start the investigation by looking to see whether the pip goes up or down from the wall opening, whether there is another outlet on the exterior wall, what happens if you pour a cup of water into the pipe (maybe squirt wit a sport water bottle rather than pour), etc. Is it a wet smell, moldy smell, a something is rotten or died smell? Not your usual sniff test, but it might give you clues what is happening ans where to look.

My first thought was a vent added for the washer drain if it wasn't tied into a vent stack and was draining slow. If so and you cap it off, you could cause another problem to reoccur.

Is that opening large enough to be a dryer vent outlet? You have one lower on that wall, but that would be close to the height where you might have a vent for a stacked washer and dryer.

Did a previous owner have a utility sink that drained there (seems high on the wall for that) -- might just dump into your washer drain.

It's going to be something unusual. Hope it's simple, like capping it off and forgetting about it.