I think it goes like this:
PCR is polymerase chain reaction. You can start with a small amount of genetic material (DNA or RNA) and keep multiplying copies so you get an amount large enough to do testing with. This is the point of PCR amplification. You put the genetic material and enzymes in a machine that cycles through stages with appropriate conditions for various stages of replication (copying).
You have a primer which will have a sequence of nucleotides matching the a unique (or relatively unique, and unique in your sample) sequence in a specific thing you're looking for (XMRV, mouse mitochondria, a criminal suspect, pGLO, a particular genetic defect, whatever). You can make any sequence you desire, synthetically. You usually have another primer for the other end of whatever you're interested in.
You put copies of the primer in with the double-stranded (or usually with doubled-over, depending on the virus) RNA (we'll say it's RNA because most viruses are RNA), enzymes, etc. You have a commercial kit which supplies the enzymes and such. The machine heats the RNA so that the parts where two strands (or two parts of the same strand) are bonded together, break apart (it's normally held together with non-covalent bonds, in this case hydrogen bonds). Then returns to a state where H-bonds are again allowed (and I think not too strongly). Now your primer can find a matching sequence on your target RNA and bind.
An enzyme called RNA Polymerase (RNA Pol for short; DNA Pol if it's copying DNA) is what copies the RNA but it can't start from scratch; it needs something to grab hold of (as it would have in a live cell situation). This is another reason the primers are useful. So it starts copying from the edge of the primer and goes until it falls off the end of the molecule.
Say unwanted parts of molecule are O, primer are P, desired portion D. (In real genetic material, you would see the sequence represented by the letters C,G,A, and T in DNA or C,G,A, and U in RNA), and matches would look like this:
3'CGCUCGA5'
5'GCGAGCU3'
For simplicity, I'm going to match like this:
OOOPPDDDPPO
OOOPPDDDPPO
please ignore the dashes (leading spaces aren't working) and spaces (not sure what makes those) and not-quite-matches
Starting DNA:
OOOOOOOOOPPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPOOOOOOOOOOOOOOOOOOO
OOOOOOOOOPPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPOOOOOOOOOOOOOOOOOOO
First cycle: (green is the copy)
OOOOOOOOOPPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPOOOOOOOOOOOOOOOOOOO
-------------PPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPOOOOOOOOOOOOOOOOOOO
OOOOOOOOOPPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPP
OOOOOOOOOPPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPOOOOOOOOOOOOOOOOOOO
Second cycle: (purple is the new copy)
OOOOOOOOOPPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPOOOOOOOOOOOOOOOOOOO
-------------PPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPOOOOOOOOOOOOOOOOOOOO
-------------PPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPP -------------PPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPOOOOOOOOOOOOOOOOOO
-------------PPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPP
OOOOOOOOOPPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPP
OOOOOOOOOPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPP
OOOOOOOOOPPPPPPDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDPPPPPOOOOOOOOOOOOOOOOOOO
With all these loose ends, you can get strands stuck together that you didn't intend. Maybe if you didn't select your primers carefully, you could end up with fragments, or maybe there's recombining RNA/DNA, and thus the variations?
