This is from the babycentre website:
Why induce?
The reason obstetricians worry so much about "post maturity" (going over your dates) is that the very small number of babies who die unexpectedly while they are still inside the womb increases after 42 weeks of pregnancy, and increases again after 43 weeks. However, the numbers are still tiny -- the risk of stillbirth is about 1 per 3,000 ongoing pregnancies at 37 weeks, 3 per 3,000 at 42 weeks and 6 per 3,000 at 43 weeks. Obstetricians aren't sure whether more babies die because the pregnancy has gone on a long time or because there's something wrong with the mothers or babies that makes the pregnancy go on an unusually long time.
Are there risks associated with inducing labour?
Medical methods of induction may not work straight away. You may need repeated treatments and it may be several days before you go into active labour.
Artificial rupture of the membranes (ARM) is not always effective, and, once your waters have been broken, your baby could be at risk of infection so your midwife and doctor will want to keep a close eye on you. If they suspect that you have an infection, you will be offered antibiotics and a Syntocinon drip.
Syntocinon can cause strong contractions and put your baby under stress, so continuous electronic monitoring is necessary. Some women also say that the contractions brought on by Syntocinon are more painful than natural ones, so you may choose to have an epidural for pain relief. You are therefore less likely to be able to move around freely during labour if you are attached to a fetal monitor and a drip for the epidural. However, some hospitals offer telemetry (where you aren't attached to the monitor by wires) and mobile epidural, which may enable you to maintain some movement during labour as well as relieving the pain.
You are more likely to need a forceps or ventouse delivery following an induction, or a caesarean. This may be due to complications in the pregnancy that led to the induction and/or it may be due to problems caused by the induction itself.
There is also a very small risk that, if a Syntocinon drip is used to induce or augment labour, your uterus may be overstimulated. This would seriously reduce the oxygen supply to your baby and could, in a worst-case scenario, cause your uterus to rupture (tear). This is more likely if you are having a trial of labour following a previous caesarean section. (See more on vaginal birth after a caesarean, also known as VBAC.)