Bracketing as in the old definition, is simply several shots (advancing the film between shots) while selecting different exposures (either aperture or shutter speed in the case of film) to increase one's chances that at least one exposure would turn out well (after processing).
</geezer hat on> Back in the 'good old days', before there was auto anything, or aperture priority, or shutter priority, or 'scene' modes like sports/landscape/portrait, EVERYTHING had to be manually set. Once a film was chosen and loaded into the camera, its ASA speed (ISO speed, these days) was essentially unchangeable until another roll of film was loaded, which may (by choice) have a different ASA speed.
So that left only the aperture and shutter speed to be manually set by the photographer. Most photographers (myself included) carried a light meter to manually meter the situation and make my settings as appropriate. For the 'really important' shots that =had= to have a good result, photographers would bracket (change the shutter speed and/or aperture) in steps either up, down, or both ways (typically a fraction of a stop) at a time to ensure a good, or best exposure. Back then as today, light meters can get fooled and can come up with a less than great result. In my own experience, I was at Disneyland in Anaheim CA in 1977 and was in front of the Magic Kingdom castle at dusk. Using a trash receptacle as a 'tripod', I took perhaps 5-6 shots of varying shutter speeds, in seconds, as I was using f16 to ensure a good depth of field. 5 of the 6 slides were trashed and I kept the best. In Washington DC one summer night, I took some shots of the US Capital and its reflection in the reflecting pool, again using a trash receptacle as a tripod as my shots were in the 10s of seconds long. Again, I took maybe 6-10 shots, and actually kept 2 or 3 of them, as the amount of darkness-hidden details 'came to light' with the longer exposures.
THAT was what bracketing was in the 'good old days'. </geezer mode off>
These days, many cameras can automatically bracket an exposure, at either a whole, 1/2 or 1/3 stop slower and faster, depending on menu settings. But that only produces 3 total exposures, and typically (maybe always?) various only the shutter speed, not aperture or ISO speed. Check your camera user manual for a complete description. But, as in my film examples, 1 stop either way may not be enough. However, for many HDR situations, it is probably sufficient.
However...
Automatic bracketing is not a substitute for understanding the basic exposure triangle. Based on the OPs original post, it seems to me that he is shooting in manual mode without understanding that his shutter speed is too slow (no tripod and shaking). Bracketing should be used for 'insurance' or HDR, not 'spray and pray' photography.