Effectively, yes. "Electrolytes" is a collective term for the ions that help move stuff into and out of your cells. These are primarily sodium and potassium, although calcium also plays a role. Sodium is the most important of these for sports drinks, because it is the one you most lose through sweat.

Unfortunately, most sports drinks don't really contain enough to balance out heavy sweating, because sodium salt (aka normal salt) tastes, unsurprisingly, salty. If a drink had the right balance of sodium, it would be noticeably salty. Gatorade has one line of drinks that do that, and Pedialyte is specially made for the correct balance. Sports drinks really jack up the sugar to help hide the salt taste.

Most sports drinks, rather than having the sodium you need to replace sweat, instead jack up the potassium (think Prime and it's advertised 843mg of electrolytes, 700mg of which is potassium). This doesn't really replace the electrolytes you need, but it also doesn't make the drink nearly as salty.

When you see "electrolytes", you should flip around to the nutrition label, which must list the actual amounts of sodium and potassium. This will tell you if it will actually help you recover from activity, or if it's just more sugar water and advertising.

Edited to add:

why is sodium so important? Because your cells use a mechanism called "osmosis" to move water back and forth. Water molecules naturally move from areas of high concentration to areas of lower concentration. In the cell, this means that water will go in to the cell if the inside of the cell has more sodium than the outside, and leave the cell when the outside has more than the inside.

When you sweat, two things happen: you lose water and you lose sodium you lose more water than sodium, so your blood becomes saltier. Water moves from inside your cells to your blood; this is what it means to be "dehydrated". To counter it, you need to dilute your blood and increase the amount of sodium in your cells. Hence, drinking water with sodium can help replenish both and speed recovery from dehydration.

Salts. Sodium, potassium, and magnesium. Edit: Not interchangeable. All three are essential.

Gatorade is a bad source of electrolytes. It's loaded with sodium but that's about it. You're better off drinking coconut water and taking a magnesium citrate suppliment for hydration. Stay away from Gatorade. It's sugar water.

EDIT: Yes there are others too. Chloride, Calcium, Phosphates, and Bicarbonate. I only mentioned the major ones. Apologies for that.

They're what plants crave

When you sweat, you lose more than just water. You also lose salt and some other minerals. Basically that's what electrolytes are and what's replaced with sports drinks.

What's not been mentioned yet is a real electrolyte drink is noticeably salty and does not taste very good. Gatorade and other sports drinks you find in the convenience store jack up the sugar to make it more palatable and saleable to the masses.

It's what they use to make Brawndo!

https://youtu.be/kIZ9YuPm_Ls?t=56

Electrolytes are chemicals that can ionize to carry current. Table salt is one electrolyte, but potassium and magnesium salts are also required by the human body. Nerves work by sending electrical signals, so they need these electrolytes in order for them to carry those signals throughout the body. The problem is, the amount of electrolytes available to nerves depends on the amount present in the bloodstream, and when sweat glands pull water out of the bloodstream, they also take some electrolytes with it. That's why you need to replenish them after sweating. If you don't, your nerves won't work as well and your muscles will have a hard time coordinating. The specific ions you need to organize muscle contraction are sodium, potassium, and magnesium, so if you're low in any of those, then you risk weakness and cramps. So it's not quite as simple as just drinking table salt.

(https://en.wikipedia.org/wiki/Electrolyte)

I once was told my mother's electrolytes were high AND she needed vitamin D because she didn't get much sun. Somehow my young brain merged the two concepts such that if someone said there electic-lights were low, I would offer them my lamp to sun with.

When dissolved in water many atoms and molecules have some charge, that allows them to create relatively weak bonds with waters (therefore stay in solution).

The charge means that they have either more electrons than protons (negatively charged) or less (positively charged). These are called electrolytes because they can be "moved" in water and separated by applying an electrical field (electrolysis, this requires a different eli5, take it as it is).

Outside water these substances aggregate to form "salts".

Now, some of these charged elements are crucial for functioning of basic biological processes, such as thinking, muscle contraction (including heart), even sensing.

Unfortunately they are lost when sweating (they are dissolved in sweat). In a healthy diet, where you eat enough fruit and vegetables, this is not an issue. If you are doing intense exercise however, an additional dose of these substances might help. TBF I am not sure if it has ever been proved that it is necessary... But it might help.

As said, if your diet is good, you don't need them. If your diet is s*it you'll probably have other issues. If you have real issues your doctor will tell you how to address them.

Tl;dr: those drinks are marketing stuff. They might be beneficial only in case of intense physical exercise, not needed for daily life if you follow a healthy diet