Let's go for another try at explaining.
Assume the universe is a sheet, and we are at the center of it. No matter how big the sheet is, we can only see a total distance away from us which is calculated as "Age of Universe * Speed of Light". So if the Age of Universe is 13.7 Billion Years, we can see anything that exists in a distance of 13.7 Billion Light Years.
However, the universe isn't a sheet. It's a rubber sheet, that someone is pulling it. The further away the point is from us, the faster it moves away (
Hubble's Law). If the distance is great enough, the point will be moving faster than light in relation to us, even though the point itself won't be moving in a faster than light speed (
see here).
So, a point that was 6 billion light years away from us when the universe was 6 billion years old may now be at 20 billion light years away, which even though is outside our observable range, it was not outside it before.
The layman's term would be that we take a photo now, but by the time we develop it, the object has moved further away.