Suppose there are two people that we're interested in (and three parties):
- Andrew would vote 1 Lib Dem - 2 Labour
- Dave would vote 1 Tory - 2 Lib Dem
So Andrew has said "I would rather the Lib Dems and if I can't have them I would rather Labour", and Dave has said "I would rather the Tories and if I can't have them I would rather Lib Dem".
Now, there are also 50 million other voters, and they also vote, and the Lib Dems come last. Now it's just Labour vs Tory, and Andrew vote ends up being counted for Labour and Dave's for the Tories.
But in this second round, they've both still been counted - they've both said which they'd prefer in this situation, and that's what their vote is counted for. This seems to be a language issue that the No campaign are exploiting: because Andrew's vote is re-interrogated to find the second preference, it is in a strictly literal sense being counted a second time. The No campaign are happy to describe it as such, in order provide the illusion that Andrew's vote in some sense outnumbers Dave. But it doesn't - every time that Andrew's preference is brought to bear, Dave's vote is also counted against it.
[Edited to take out some editorialising - vote as you see fit, I just wanted to clear this up]