Why are salt and pepper such universal seasonings across the world?

Salt is biological. Your nervous system uses electricity. Electricity cannot travel through pure water, it needs needs something like salt to do that, and small amounts of salt are non-toxic. Without salt your brain would shut down and you'd die. So we evolved to crave salt.

Pepper is cultural. It is native to India and only grows in tropical regions so once upon a time it was really expensive stuff in a place where it couldn't be grown or easily shipped-- like Europe. Garnishing your food with black pepper was, at one time, a status symbol comparable to eating ice cream with 24-carat gold flakes on it. Which, by the way, people do. 

Pepper basically said, "I'm a big deal, not only can I afford food, I can put black gold on it." Also, pepper was literally called "black gold" in its heyday. Today pepper is popular for the opposite reason. It's cheap, readily available and perhaps most importantly, it's expected.

Salt has been important for a very long time. Civilizations were built on the salt trade (check out the Muisca). Pepper is awesome and was a big status symbol of it's day, I can't really explain why it's expected on every table today apart from what other people have said about it's history.

But I can add that there are a lot of other seasonings which aren't as popular as salt and pepper. There can be any reason why this is the case depending on which one, but I want to talk about monosodium glutamate, or MSG. Glutamate was discovered to be a primary source of flavour by a dude named Kikunae Ikeda. He was trying to figure out why his broth tasted so damn good, identified that the kelp in it was the source of the awesome flavour, and then discovered that glutamate was the important ingredient.

The sodium salt form MSG was quickly commercialised and has been a staple seasoning in Japan ever since. If you have a Japanese snack with "amino acid seasoning" in the ingredients list, I'd bet my left nut that includes glutamate. So this stuff is naturally found in most food, it is an essential amino acid after all, but using the salt as seasoning fell out of favour in places like the USA or Australia. Reason being people complained about "Chinese food syndrome" or "MSG allergies." Conditions which we aren't yet sure actually exist, as the evidence for them is mainly anecdotes about very subjective symptoms like "feeling hot." Maybe there is an allergy or reaction that only non-Asian people get. I suspect however that it's another health scare against substances viewed as foreign or artificial.