The basic element. You can find them all around the map at the start of every big structure, and sometimes even inside if those structures are big. Check out Prinz's useful map guide to find out where all of them are placed.
You can easily locate them from a distance by the light blue beam they emit, even if not activated.
If you get close to one of them, they will turn on, you will regen full health and your progress will be saved. The next time you lose all of your three lives, you will respawn next to the lantern. Basic ennemies and pots will be regenerated too.
You can also use the Warp function in the pause menu to teleport to the last lantern you activated.

While not visible, there are some hidden respawn points in the desert. These are generally placed near a structure or a place where you can die while riding a sand shredder, while far away enough from your lantern.
If you die after trigerring one, you will respawn at full life at its position instead of your normal respawn lantern. However, the lantern you last interacted with will not be deactivated and if you try warping, you will teleport to the lantern.

If you stand still for a second and are not affected by any moving element or enemy, your position will be saved in case you fall into the void or quicksand. You will teleport back there if you had at least 2 lifes left but you will not regain health. Of course if you fall into the void or quicksand with 1 life left, you will respawn to a lantern or a point, and that last safe position will be forgotten.

You do not need to activate every lantern you come across, in fact you can skip them entirely. This way, you only keep the lantern you want activated and can use the warp function for a quick travel anytime anywhere.
This also means that if you die, you will respawn to the last triggered respawn point (and not your lantern), which can be annoying at times and isn't recommended if, for example, you are discovering a structure for the first time. Use it only for cases like if you want to quickly grab easily accessible coins you've missed, and then teleport to get out of the structure and closer to the other ones.
This technique is also used in speedruns.

The point of this technique is to avoid redoing entire segments of parkour if you ever miss or fall.
Basically, as long as you don't stand still for long enough, your last safe place position won't be saved, and you can use this to your advantage. You will need at least 2 lives for this.
Before a complicated part, stand still for a moment to save your position, and make an attempt. If you ever fall or miss something, try to get to the nearest quicksand/hole that goes to the void. If you touched the ground, do it while constantly bunnyhopping. The time or distance won't matter as long as you keep bunnyhopping.
This way, you will lose a life, but you will teleport back to the nearest safe position. And if you did it correctly, that position should be right before the part you just failed, and you can make another attempt quicker without having to redo all of the previous parts.
This technique is also used in speedruns.

If you have at least 2 lives and you warp back to your lantern right before you fall and die to quicksand or the void, you will teleport twice : one time to the lantern, and right after it to your last safe position. You will regenerate all of your lives but lose one in the process (due to falling and dying).
This can lead to funny glitches like being inside a pot (break a pot, stand where it was to save your position, then bunnyhop to the nearest pit/quicksand and perform a double respawning. The pot will reappear, and you will respawn inside of it), or help get back up to that hard part you were trying before dying, with two lives again (untested, i just thought of this now).
The timing can be tricky, as you need to trigger the death animation before the warp animation finishes, otherwise you will teleport twice to your lantern (because if the warp animation finishes first, you will teleport to your lantern and touch it. So it will set your new respawn position there)

I hope this helped ! Thank you for reading