When you train hard in the gym, especially when you train to failure, you will notice two things: 1) a burning feeling, and 2) a swelling of the muscles. Here's how this happens and what it means for your training.
Muscle Burn
Muscle burn comes first, in a sense, because it is the first thing you feel when you are at your limit of the repetitions and, or weight you can lift. High repetitions at a lower weight will also cause the 'burn'.
The burning sensation is caused when you muscles enter anaerobic territory. Anaerobic means "without oxygen," but in exercise physiology it really means that your muscles' demands are such that your oxygen intake and supply cannot meet the demands of the muscle. In this anaerobic scenario, acid conditions and the production of hydrogen ions build and you get the burning feeling when the nerve cells and receptors are impacted.
In years gone by the burning sensation was thought to be caused by lactic acid / lactate, which is produced under these conditions. But we know now that lactate is probably a helper response, an attempt by the body to remove these hydrogen ions.
Training helps your muscles deal with this acidic environment and athletes who must compete in this anaerobic state need to train in that environment as well. Muscle builders and bodybuilders utilize the burn in order to enhance muscle development. Lactic or at least acidic metabolic conditions seem to assist the growth of muscle.
The Pump
Following a weight training session you may notice a feeling of "fullness" in the muscles. This is not quite "swelling," which implies a medical condition, but definitely a feeling of increased size, which is also visually noticeable. This is "the pump."
The pump is caused by blood plasma getting trapped in the spaces between muscle cells by the action of muscle contraction. It probably lasts for about 30 minutes or so, to some degree, after your session is complete. Bodybuilders will use it to sharpen up definition just before going on stage to be judged.
This does not seem to have any adverse health effects, however you do need to maintain adequate glycogen (glucose) stores and be well hydrated to ensure a good pump. Low-carb diets will not be a good approach.