Okay, let me have a crack... As mentioned, they are indeed viruses. We can see them in their original form and can (and have already) observed them infecting uninfected cells in a lab. The following ascii art is rudimentary, but hopefully it makes sense.
Imagine this is the dna strands of a handful of cells in a petrie dish...:
1 aaaaaaaaaaaaaaaaaaaaaaaaa
2 aaaaaaaaaaaaaaaaaaaaaaaaa
3 aaaaaaaaaaaaaaaaaaaaaaaaa
4 aaaaaaaaaaaaaaaaaaaaaaaaa
5 aaaaaaaaaaaaaaaaaaaaaaaaa
Then, we introduce our retrovirus(R) to see how it infects cells in our dish, this is what we see...:
1 aaaaRaaaaaaaaaaaaaaaaaaaaa
2 aaaaaaaaaaaaaaaaaaRaaaaaaa
3 aaaaaaaaaRaaaaaaaaaaaaaaaa
4 aaaaaaaaaaaaaaaaaaaaaaaRaa
5 aaaaaaaaaaaaaaaaRaaaaaaaaa
In short, the retrovirus can infect the cell's dna at any point, and this bears out in every test we've ever done. If we isolate one cell that the retrovirus doesn't kill via infection and culture it, we get a unique identifying marker in all of its offspring...:
1a aaaaRaaaaaaaaaaaaaaaaaaaaa
1b aaaaRaaaaaaaaaaaaaaaaaaaaa
1c aaaaRaaaaaaaaaaaaaaaaaaaaa
1d aaaaRaaaaaaaaaaaaaaaaaaaaa
1e aaaaRaaaaaaaaaaaaaaaaaaaaa
If we introduce another retrovirus(X) to this new dish of cells, we see this...:
1a aaaaRaaaaaaaaaaaaaaXaaaaaaa
1b aaXaaRaaaaaaaaaaaaaaaaaaaaa
1c aaaaRaaaXaaaaaaaaaaaaaaaaaa
1d aaaaRaaaaaaaaaaaaaaaaaaXaaa
1e aaaaRaaaaaaaaaXaaaaaaaaaaaa
Again, the new retrovirus is infecting the cells at random locations, exactly the same as retrovirus(R) did previously. Providing the new retrovirus doesn't kill the cell, we now have Two unique genetic markers (ERVs) that will be inherited by subsequent offspring of these cells. Knowing how viruses infect cells dna and knowing how dna is copied on reproduction, we can work out the odds of any given cell's dna profile being the progeny of any of these cells above. Here's some examples of cell dna we can reasonably calculate to be the offspring of our experimental cells above...:
Example A - aaaaRaaaXaaaaaaaaYaaaaaaaaaa - This cell has a new unique endogenous retroviral remenant(Y), but we can calculate the odds of this cell to be the offspring of the cell experiment 1c to be around 625:1, or 99.984% (calculated on 1 in 25(squared) chance for each infection to be a coincidental infection at the same locus instead of inherited). Let's call this new sample 1c1.
Example B - aaXaaRaaaaaaaaaaaaaaXaaaaaaa - So, this cell has something different.... almost as if it's the progeny of two cells mating(?) In this case, we can see the DNA profile is likely to be the product of sexual reproduction of 1a and 1b! By using our 1 in 25 chance of coincidental infection versus inherited trait, we can calculate the odds of this cell's parentage - in this case, 1a is 96% likely a parent (with one matched marker) and 1b is 99.984% likely a parent (with two matched markers). So, we can name this sample 1ab!
So, now you've seen this very rudimentary layman's explanation, let's test your understanding & see what you can tell us about the following cell dna profiles....

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Example C - aaaaRaaaXaaaaaaaaYaaaaaZaaaaa
Example D - aaaaRaaaaZaaaaaXaaaaaaaaaXaaa
Example E - aaaaRaaaXaaaaaaXaaYaaaaaaaaaa