Tortoises vary in size and shape and to some degree in their internal structures, but in general, the pictures and details offered below will be largely accurate, and at least offer a place to start learning about the internal and external features of your tortoise.
Tortoises' spines are attached to their shell, which is composed of carapace (the top portion) and plastron (the bottom portion).
All of these parts grow for the tortoises' entire lives, although obviously they grow more rapidly (and to a proportionately greater extent) in their early years; this is why a proper balance of calcium in their diet is so important, and why the wrong foods (or even the right foods in the wrong amounts/proportions) can lead to problems in their growth and health and longevity.
Their internal organs are mostly quite similar to what you'd find inside of your own body in arrangement and function.
The reproductive systems are different in reptiles than in mammals, and in tortoises do not normally express until they reach adulthood.
The digestive tracts of tortoises vary based on their nutritional needs and design: herbivorous tortoises have longer intestines to support the breakdown and fermentation of the foods they eat by their digestive microbiomes; omnivorous tortoises have shorter overall intestines that can break down a wider variety of foods, including more sugars and protein than their herbivorous relatives. It's important to feed tortoises the proper foods in the proper proportions to assure healthy growth and long life.
Tortoises are cold-blooded animals, which means that they get the warmth they need from their environment, rather than creating it by burning calories as warm-blooded animals (like humans) do; this is an efficient design, letting them spend their energy in other ways, but also limits where and how they can live.
In captivity, tortoises need heat provided for them by us, generally in the form of some combination of real (or fake) sunlight (which should also provide ultraviolet energy, which nearly all animals need in some quantity) and heating via various heat emitting hardware.
Every kind of tortoise has an optimal temperature range, in which their digestive and other systems all work best... keeping a tortoise outside of that optimal temperature for too long can be dangerous, even deadly.