One thing I should mention is that these distances are all a bit arbitrary. How far away something is depends entirely upon what you mean by "distance".
If you want to get into the nitty gritty details, here is a rundown of all of the major distance measures used in Cosmology:
A couple of examples of the available distance measures are:
1. Luminosity distance: let's say you want to judge distance by comparing against the brightness of objects. In 3-dimensional space, objects' brightness drops off as 1/r^2. So if we know the intrinsic brightness of something, we can measure how far away it is. The "r" here is the luminosity distance.
2. Angular diameter distance: if we know how physically large something is, and then compare it to how large it appears on the sky, then that's another measure of distance. Here the angle that the object subtends on the sky drops off as 1/r (for small angles), and this "r" we can use as the angular diameter distance.
3. Comoving distance: If we take a hypothetical situation where we stop the expansion in such a way that every point in space sees the same CMB temperature, and then send some light rays around, the comoving distance is the time it takes for those light rays to get from place to place.
It's this last one that people usually use when talking about distances to the public.