I assume you are talking about population genetics. It means that when population is greatly reduced (whatever the reason) some mutations/alleles that were not necessarily favorable/frequent in the original population might come to represent a significant amount of the population because it survived better (by chance or not) during the population reduction. It is very similar to the "founder effect", but with a wider application (founders are just a particular case)

Yes. The remaining genetic variation present in the 3 survivors is less than the genetic variation that was present in the population of the original 10. Picture a bottle. The thick part represents the amount of original variation. The thin neck represents the reduced variation in the survivors. This is why it’s called a bottleneck.