This is the short story.
Barometric pressure is like a sodastream machine. You need to keep the bottle / water under pressure before the water will absorb the gas. If you pump the gas into the bottle without "pressurising" it, it will absorb nothing. Same effect with the ocean. The higher the pressure the more water absorbs oxygen. If oxygen levels are low, fish will be lethargic and not eat. Just like you and me, when they haven't eaten for a while and suddenly they get an appetite, they go into a feeding frenzy. Hence the change of weather, change of feeding patterns. Cold front's have nothing to do with it but probably has more to do with the wind which a) increases the pressure and b) messes up the surface of the water allowing it to absorb oxygen. We generally have consistent weather patterns, high pressure cells and low pressure cells developing in the same areas because of fixed land / sea conditions. There fore we associate the "cold front" with "fish coming on the bite" but it probably has more to do with the wind over surface and wind direction. If the wind is pumping, conditions will change and the pressure will rise. You will also notice that guys talk about fish coming on the bite when the wind changes. It has nothing to do with it but rather when that wind changes to NE, the barometric pressure has risen. Then the NE (in Durban) messes up the surface combined with the high pressure, oxygen levels are at their highest.
Specifics on barometric pressure has been nicely laid out by Fanie in his post.
Just my 2c
Tight lines