Some people would call a pile of something on the ground, a "structure". But in this context, the term is applied to a method of containing material for the purpose of actively composting it.

It does not matter whether you call it a structure - or a containment. I call it a structure, designed to be a containment. Most folks just call it a bin. Or a multiple-bin "set" - or a multi-compartment bin. Whatever.

There are a LOT of different kinds and types and styles - and I'm not going to attempt to provide information on all of them. If you want to do something different to contain your compost pile - I encourage you to experiment and follow your inclination. Point being - whatever works for you is the right way to do it.

I have my favorite containments for various reasons.

cinderblock bins are strong and insulate the pile - I use a two-compartment bin as my "critter pile" that processes meat - including whole road kill. Front slats are 3/4" plywood and the top is covered with chain link. In this bin, I have no trouble from animals getting into it from the outside. Bones compost just fine - simply takes a bit longer. If something was alive - and it's now dead (or recently harvested) - it WILL decompose in time. Period.
Another favorite is the pallet bin. Very inexpensive, fast and easy to build - with some experience doing it, or a plan to follow. Doing it the first time with no plan can be a hassle unless you think it through.

Thinking it through - deciding which material is least expensive for the purpose, easiest to construct, and whether or not you'll be collecting leachate tea. I strongly recommend collecting tea. Why? Read the section on Compost Tea - Leachate. Then you'll understand.

Any type of containment can be designed to efficiently collect the tea - runoff from watering the pile. As the water filters through the pile it picks up soluable plant nutrients, humic content (made by microbes) and some microbial life. Concentrating the tea by putting it back through the pile is a common practice. Point being that you want to consider how you're going to get the tea out of the barrel in the ground.

Strong wire screening, with opening sizes from chicken wire down to 1/4" hardware cloth is the containment method I recommend most often, particularly to elderly folks. Because it's the easiest containment to use.

Check other links to learn details of each method.

COMPOST CONTAINMENTS
Click Here to see: Compost Containments
COMPOST PILES
Click Here to see:COMPOST PILES