It is a pregnancy that is only known from the chemical Hcg being present. Once a pregnancy is determined by an u/s or pelvic exam, it becomes a clinical pregnancy.
To add to what Alaska said, a biochemical(or chemical) pregnancy is when the embryos begin the implantation process and the shell covering the embryo breaks. Within that shell is a small amount of hCG, which spills into the bloodstream. The amount is so small that it either barely registers or nor at all on a peestick. The exact amount is detectable in blood, which is where the low beta numbers come from. I had one in August and my 1st number was 7 and the 2nd was 9. For some unknown reason, the implantation process stops (possibly, the embryos are flawed and nature takes its course), in effect ending a viable pregnancy. Like Alaska said, it is a very early miscarriage where the implantation never fully takes place.
from my experience, a chemical pregnancy is a nice way of saying 'very early miscarriage'.... so much so that in under normal circumstances, women often don't know that they are pregnant because the HCG level does not get very high, and then AF shows up.
I have had two chemicals with IVF -- my HCG never got above 15 on the first and 9 on the second. My second didn't even register on an hpt.
Hope this helps.....