Cryptographic library.
Nettle is a cryptographic library that is designed to fit easily in more or less any context: In crypto toolkits for object-oriented languages (C++, Python, Pike, ...), in applications like LSH or GNUPG, or even in kernel space. In most contexts, you need more than the basic cryptographic algorithms, you also need some way to keep track of available algorithms, their properties and variants. You often have some algorithm selection process, often dictated by a protocol you want to implement.
And as the requirements of applications differ in subtle and not so subtle ways, an API that fits one application well can be a pain to use in a different context. And that is why there are so many different cryptographic libraries around.
Nettle tries to avoid this problem by doing one thing, the low-level crypto stuff, and providing a simple but general interface to it. In particular, Nettle doesn't do algorithm selection. It doesn't do memory allocation. It doesn't do any I/O.