It means we got the sequence of As, Cs, Gs and Ts; but in practice, we don't even achieve that.
The human genome has approximately 3 billion nucleotides in 23 chromosomes. So you would think a "sequenced genome" is 23 strings over the alphabet {A,C,G,T} with a length of 130 million or so each. However, it is only possible to sequence a few hundred nucleotides at a time. So you end up with a jigsaw puzzle of tiny pieces, some containing errors, some missing, some exact duplicates of each other. Putting these back together corectly isn't even possible, doing it approximately is still difficult.
So in practice, a sequenced genome is a sequence of medium size strings, arranged in the mostly correct order, with many small and a few large gaps, so they form a good chunk of the long strings that would really be a genome. And even if all of that was completely correct, we still wouldn't know what most of these nucleotides mean.
The first "draft" of a genome is usually even worse. If you simply dump DNA fragments from a mammal onto a modern day sequencer (Illumina HiSeq), and run software to kind-of solve the jigsaw puzzle, you end up with a million pieces, each about 2000 nucleotides in length, in no particular order. Since most genes by far are longer than that, I'd say it's fraudulent to call something like that a genome, but it's being done all the time.
> Do we ever sample more than one member of a species?
Yes, but not in the same way. Instead of (approximately) solving the impossible jigsaw puzzle again (that's called de-novo assembly), we tend to compare the puzzle pieces from a new individual against the big picture we got from the first genome (that's called mapping). This way, we can see small differences (single substitutitions, small insertions and deletions), which is most of the variation present in a species. What we can't see is large scale variation, like duplicated genes, or rearrangements of large pieces of the genome, or insertions of retroviruses. We know these exist, it's just more expensive to look for them. (All of this changing as sequencing is becoming cheaper.)
Multiple individuals of a species get sequenced when there is interest. Probably tens of thousands of humans have been sequenced by now. For model organisms, the number is much lower. For pathogens, where everything is much easier anyway, the number could easily be higher.