I posted some decoded x86 machine code here last week, however I didn't really explain what it did (also because I didn't actually know yet). I found a cleaned up version of the corresponding Assembler code, complete with comments, which makes the whole thing pretty understandable.
Basically, the code consists of two parts: gaining root privileges, and then spawning a shell. Each is accomplished through a syscall (this is what the int 0x80 instructions are for). I reality, code like this might be deployed through a buffer overflow - for instance, one could flood an unchecked text input field with NOP instructions (0x90), overriding the following memory with instructions to do nothing at all (this is called a NOP slide) , and then placing the shellcode at the end of this slide, causing it to be executed and you to be prompted with a root shell.
Now, it's not quite as simple as that, after all the string (and shellcode) will only be copied into the buffer, and even if it overflows it, the code's execution is not guaranteed. For this, some function will have to actually have to jump or return to an address that lies somewhere on our NOP slide. If you want to find out in detail how to do this, I suggest you read this very excellent article on the subject.