I did a little research after I found out about our Very Imperfect Embryo and found this little gem of a website:
Turns out that the grading (in our case for this round, 4BB) relates to a few different parts of the embryo.
The first number (4) relates to blastocyst growth (what stage is it at?) also known as the expansion grade, and it tells you in this case that it is an expanded blastocyst, that the cavity is larger than the embryo, with thinning of the shell.
The first letter (B) relates to a grading of the inner cells of the blastocyst. Are they tightly packed (good) or more loosely packed (not so good). In this case the blastocyst has several cells, loosely grouped, so not ideal.
The last letter (B) relates to a grading of the trophectoderm cells (TE), which are the cells around the inner rim of the blastocyst that will form the placenta. A B grading here means there are few cells, not as cohesive a layer as an A grade embryo.
Different clinics may use varying methodologies to give you a grading on your embryos but it basically adds up to them looking at the same three things, which is the Gardner blastocyst grading system: 1) Blastocyst growth (expressed as a number between 1 & 6, 6 being most advanced), the cells inside the blastocyst and how tightly packed they are (expressed as a letter between A & C, with A being the best grading) and the cells on the rim of the blastocyst which will form the placenta (again, expressed as a letter between A & C, with A being the best grading).
It's important to remember that all of this grading only adds up to your chances of successful IMPLANTATION and has no bearing on the pregnancy once a successful implantation has taken place and the pregnancy is established.