There are many altars in Echo of the Wilds that require offerings in order to perform some function, like saving the game or learning new crafting recipes. Some altars, like those at the Plains Gateway, will only accept specific items. Others accept any edible item plus gold items, like the one at the Endly Altar. In this second case, generally if an item has high nutritional value it will give a higher chance of the altar performing its function rather than doing nothing. Gold nuggets will always succeed when offered at these altars.
Concerning the altars at the Mystical Monuments, the developer has written:
"Yeah, the way altars work is that they each have a table of items like so:
1 = Torch
2 = Stone Axe
3 = Stone Hammer
Then each food item has a value (e.g. mushrooms have 0.5, berries have 3.5). When you bestow food it then compares it the table, so in this example berries would offer the stone hammer (though there's also randomness involved).
If you already learnt that recipe then it goes down the table until it finds a recipe you haven't learnt. If it reaches the bottom of the table without finding a recipe to offer then the value of the food is saved for next time you offer food. For example, if you offered berries (3.5) but it didn't offer a recipe, then you offered mushrooms (0.5) then the combined value is 4.
So basically you're better off offering low-tier items like mushrooms, currants and milky plants, first then using berries, fish, offal, etc, later on when you've learnt a bunch of recipes from the altar."