At the bottom of the window as the programme is playing you will see a slider running from left to right. If you grab that with your left mouse button you can pull it across - and you will notice the time count increasing. Let go at the point you wish to continue watching the programme. You can also pull it in a backward direction to watch something again.
The iPlayer will also "remember" where you got to when watching a programme, and continues from that point the next time you start it.