BBC iPlayer programmes need a minimum amount of bandwidth - the amount of data that your connection can transfer - to play smoothly. If your internet connection can't handle the data rate, for example you're on dial-up internet, then you will see this message.
Check your available bandwidth using the BBC iPlayer Diagnostic tool.
You may see this message despite having an adequate bandwidth according to this tool.
There are a number of potential causes of this, including sharing bandwidth with other devices on the same connection, using wireless connection devices, and incorrect bandwidth allocation from your router.
Check the quality level at which you are watching. HD or higher quality needs more bandwidth and processing power. Try switching to normal or lower quality (located on the bottom left of the programme page) to see if this helps.
If you have checked these possible causes and are still told you have insufficient bandwidth, you should contact your ISP (internet service provider).