Most women go into labour naturally by the time they're 42 weeks pregnant.
If your pregnancy lasts longer than 42 weeks and you decide not to have your labour induced, you should be offered increased monitoring to check your baby's wellbeing.
There's a higher risk of stillbirth if you go over 42 weeks pregnant, although most babies remain healthy. At the moment, there's no way to reliably predict which babies are at increased risk of stillbirth, so induction is offered to all women who don't go into labour by 42 weeks.
Having induction of labour after the date your baby is due doesn't increase the chance of having a caesarean section. There's actually some evidence it may slightly reduce the chance of having a caesarean section.