can someone explain the string of letters that appear after the PC.

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You mean the CPU capability detection? As in your case:

AMD Athlon(tm) 64 Processor 3200+ [x86 Family 15 Model 47 Stepping 2] [fpu tsc pae nx sse sse2 3dnow mmx]

FPU = Floating Point Unit.
TSC = Time Stamp Counter. (is used whenever possible to further improve the accuracy of the speed measurement.)
PAE = Physical Address Extensions. (is the added ability of the IA32 processor to address more than 4 GB of physical memory.)
NX = No eXecute. (the ability to not run code.)
SSE = Streaming SIMD Extensions. (70 new Single Instruction, Multiple Data instructions built in in the CPU.)
SSE2 = See SSE. (An additional 144 SIMDs.)
3DNow = a multimedia extension created by AMD for its processors, based on MMX.
MMX = MMX is rumoured to stand for MultiMedia eXtension or Multiple Math or Matrix Math eXtension, but officially it is a meaningless acronym trademarked by Intel.

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