A buzzing or whining boiler noises coming from your boiler could indicate that there is an issue with your boiler pump and a part on it has seized up.
If you put your hand on the pump it should be warm to the touch but not hot. If it is hot, then there is likely an issue with an internal part.
Call a Professional
There are many different noises that your boiler can make such as humming, banging, ticking,buzzing, vibrating and while some of them can seem worrying at first, most can easily be fixed. If you are unsure about any noise your heating system is making, the safest thing to do is call a professional.