Often when working close to the hardware or when trying to control the size/format of a data structure you need to have precise control of the size of your integers.

As for u8 vs uint8_t, this is simply because Linux predated <stdint.h> being available in C, which is technically a C99-ism, but in my experience is available on most modern compilers even in their ANSI-C / C89 modes.

Adding my 10 cents to this answer:

u64 means an 'unsigned 64 bits' value, so, depending on the architecture where the code will run/be compiled, it must be defined differently in order to really be 64 bits long.

For instance, on a x86 machine, an unsigned long is 64 bits long, so u64 for that machine could be defined as follows:

typedef unsigned long u64;

The same applies for u32. On a x86 machine, unsigned int is 32 bits long, so u32 for that machine could be defined as follows:

typedef unsigned int u32;

You'll generally find the typedef declaration for these types on a types.h file which corresponds to the architecture you're compiling your source to.