I read somewhere, most likely on one of these forums, that meyer lemon seeds do not grow meyer lemon trees. The same goes for other kinds of citrus that do not come true from seed.

But then the question is - what does come out of these seeds?

Could be many types of gene combinations. However, usually it is more or less a fruit similar (but many times inferior) to the Meyer lemon. Clementine Mandarins also do not come true from seed. I have grown a lot of Clementine seedlings, with all of the resulting fruits being similar mandarin type fruits. This is probably because Clementines are normally grown in monoculture blocks of 100 percent Clementines. - Millet (924-)

It will be a cross between the Meyer lemon and the pollen parent. However, if the pollen parent is also a Meyer lemon that does not mean the offspring will be identical to a Meyer lemon - just like people. The offspring will have half its genes from each parent but not the same half for each seed. Most citrus cultivars produce seeds that are genetic clones of the mother tree and do not include any genes from the pollen parent.

I posted about my experience with Meyer Lemons here,
link
Basically, they seem to be fairly variable Citron to Lime types.
The Meyer is thought to be a hybrid, parents unknown, possibly a mix of 2 or 3 types. Even self pollinated seed lots of complex hybrids should show a lot of variation, just by shuffling the genes of the original parents. Clementines may not be as widely hybridized, they might be mandarin X mandarin, so if self pollinated less variation can appear, and the seedlings still closely related.

For any citrus seeds that do not come true, the result will be similar to the parent, but there are many factors in play here--the plant's vigor, the shape, size, color, taste, disease resistance, and productivity. There is always a chance of a new variety that will rate high in all of those factors, but there is a much higher chance that at least one of those will be rated poor.