Burn sensation in muscles is general indicator, that you've been working our beyond your Anaerobic Threshold for some time. It means, that your body can't eliminate the exertion of lactic acid. It usually happens with runners, cyclist, etc.
The anaerobic threshold (AT), the point at which lactic acid starts to
accumulates in the muscles, is considered to be somewhere between 85%
and 90% of your maximum heart rate. 
But why pain or burn is felt ? It's because of the acidity of lactic acid, which is made of (non-acidic) lactate and (acidic) hydrogen ions:
The breakdown of glucose or glycogen produces lactate and hydrogen
ions (H+) - for each lactate molecule, one hydrogen ion is formed. The
presence of hydrogen ions, not lactate, makes the muscle acidic that
will eventually halt muscle function. As hydrogen ion concentrations
increase the blood and muscle become acidic. This acidic environment
will slow down enzyme activity and ultimately the breakdown of glucose
itself. Acidic muscles will aggravate associated nerve endings causing
pain and increase irritation of the central nervous system. The
athlete may become disorientated and feel nauseous 
Very high levels of H+ can damage cells, so, long term training beyond the anaerobic threshold is not an good idea :)
Burn sensation can be used as indicator in endurance trainings or during high performance interval training -- but anyway, it means that you've reached you limit and you need to lower the intensity to 40-50% to eliminate the extra acid.
You didn't specified your goal, but I assume that it's strength or common fitness. So, lower the intensity when you feel that your muscles are burning and do not use it as indicator in strength training.