The cord blood is the blood and umbilical cord that is cut from the infant right after delivery. Typically, it is thrown away after birth. However, now we know that it contains adult stem cells. It actually contains the SAME type of stem cells that are also in your bone marrow (its the stem cells in the bone marrow that make a bone marrow transplant work).
Cord blood banking takes the cord and blood, perserves it, and freezes it until (if) its needed. At the time its needed, it can be dethawed, used in a bone marrow transplant, or a handful of other treatments.
Long story short.... If you have the money to spare, its a great thing to do. If you dont have the money to spare, dont worry about it. There are other alternatives if the child gets sick, including a public cord blood bank, and a world wide marrow donors registry.
In the US, it costs about 2000+ initially, and then a couple hundred per year.
If you dont privately bank, you should consider donating, which is free for you.
For information regarding your area specifically, ask your gynocologist for advice.