ICSI, or intra-cytoplasm sperm injection, is a procedure where the embryologist injects a sperm into the egg.  There are a number of reasons that this is done, the most common is for men with very reduced semen parameters (low sperm concentration and/or motility)
It is routinely done if the sperm is retrieved from the testicle, testicular sperm extraction (TESE).  There are men that have no sperm in the ejaculate, sometimes because the testicle is not making enough sperm to survive 90 days and be present in the ejaculate.  There are men who are born without a vas deferens, a condition known as congenital absence of the vas deferens (CAVD) which can be associated with certain forms of cystic fibroses. There are men that have had a vasectomy, and reversal of a vasectomy is likely to be unsuccessful, or a reversal was performed, but was unsuccessful.
There are times that the sperm are retrieved from the epidydimus, with micro-surgery, and ICSI is performed with this sperm as well.