Circuitsmith gave a pretty good answer. Changing exhaust back pressure can change the overall fuel mixture in carbureted engines…If you are talking about taking the muffler(s) off a modern fuel injected engine with a converter and two oxygen sensors ahead of the muffler, then it will not make any difference except in noise level. The forward oxygen sensor will keep tabs of the fuel mixture and adjust it as needed to keep exhaust gas temperature in the safe range…(a lean mixture will burn very hot).
Racing engines usually use a tuned exhaust system, which utilize headers and a megaphone to aid exhaust gas extraction. With these parts in place, the fuel mixture is carefully set on a dyno for optimum performance and to avoid burned valves…
Harley owners who routinely remove their mufflers usually must have their carburetors re-jetted to compensate for the change…Harley shops, who have done thousands of these removals have become expert at selecting the proper jets and installing them…