Many practical optimisation problems are less like "let's go hiking and climb a literal hill which we can see in front of us" and more like "find the best design in this space of possible designs that maximises some objective"

Here are some alternative example problems, that are a lot more high dimensional, and also where the dimensions are not spatial dimensions so your eyes give you absolutely no benefit.

(a) Your objective is to find a recipe that produces a maximally tasty meal, using the ingredients you have in your kitchen cupboard. To sample one point in recipe-space, you need to (1) devise a recipe, (2) prep and cook a candidate meal following the recipe, and (3) evaluate the candidate recipe, say by serving it to a bunch of your friends and family. That gets you one sample point. Maybe there are 1 trillion possible "recipes" you could make. Are you going to brute-force cook and serve them all to find a meal that maximises tastiness, or is there a more efficient way that requires fewer plan recipe->prep&cook->serve->evaluate cycles?

(b) Your objective is to find the most efficient design of a bridge, that can support the required load and stresses, while minimising the construction cost.