Premium Bonds are a form of investment that includes a little luck and a little gamble. It is similar to a lottery but the stake, your investment, remains available to you to cash in and is secure being invested with the government.
The interest element is the potential prizes you may win. The amount allocated to the prize fund is based on a set percentage of the amount invested in the total savings fund. The interest rate changes broadly in line with Bank Rate.
Premium Bonds can add a bit of fun to your investing portfolio but they do have some significant advantages over other investments. Compared with the National Lottery the main benefit is that it is automatically entered each month and you get one entry per month per bond held at the cost of not getting interest on the money invested in your premium bonds. However winnings are not subject to income tax or capital gains tax and this may be particularly beneficial for certain people.
If you are a high tax payer then any returns are more valuable because you pay no tax. If you receive tax credits then any savings you have in premium bonds appear to be irrellevent to your tax credits. Check this yourself but this is my understanding at this moment.
In a purely financial sense there may well be better investments available but the benefits of a bit of fun, the security of your investment and the tax benefits may make Premium Bonds attractive for you.