OS BITS ON LINUX/DEBIAN 64 or 32 bit
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So your on this step of your debian install: http://www.debian.org/CD/http-ftp/#stable
When you pick the debian distro to download it asks for

amd64 armel armhf i386 ia64 kfreebsd-i386 kfreebsd-amd64 mips mipsel powerpc sparc s390 s390x source multi-arch

If your a simpleton your probably just have an AMD or INTEL process thats either 32 or 64 bit. So lets break down what you need:

amd64: even though it says amd, if you have an intel 64 bit process or an amd 64 bit processor you need to pick this
i386: even though it has i which stands for intel, this will work with amd. This is for 32 bit processors of the AMD or INTEL type
ia64: This is for itanium processors, so thats not us – this does look like it belongs to intel 64 bit, but its not really as much intel as it is itanium

The others are for devs and other reasons. Sparcs are for sparc units, Source is for source code if you wanna compile one of these your self.

So there you have it:

INTEL 64bit: pick amd64
AMD 64bit: pick amd64

INTEL 32bit: pick i386
AMD 32bit:pick i386

Why is it called amd64? because amd pioneered 64 bit and intel then took on the race, but now adays its the same or whatever so your good with picking that.

Of course for your 64bit processors you can go with the i386 32 bit systems.

By the way another terminology for all this is covered in this sentence:
You want AMD64, as that’s the “normal” x86-64 architecture (in the same way that i386 is the “normal” x86 architecture and will run on AMD CPUs). You can of course use the 32-bit version of Debian, if you wish (i.e. i386).
Which I got from Nylex from http://www.linuxquestions.org/questions/debian-26/amd64-or-ia64-705311