The main use for bicarb - sodium hydrogen carbonate, which used to be called sodium bicarbonate - is when doing a fishless cycle with soft water. There are a couple of reasons.
Soft water usually goes hand in hand with low KH - that is, not much carbonate. The bacteria we want to grow in the filter (and elsewhere in the tank) need inorganic carbon to multiply well. Carbonate is the usual source of inorganic carbon in tap water. There's lots of it in hard water but not much in soft water. If we can add carbonate during fishless cycling, the bacteria multiply better.
The cycling process makes acidic things - nitrite and nitrate. If there isn't much KH, it gets used up and the pH falls. At pH below around 6.5, the filter bacteria stop multiplying, which is not good if we are trying to grow a lots more of them. Adding bicarb - a form of carbonate - means there is too much carbonate to get used up so the pH doesn't drop. My tap water KH is 3 degrees, just below the relatively safe level of 4 deg. During my first fishless cycle I did not add any bicarb at the start and the pH dropped off the bottom of the scale. The second time I did a fishless cycle, I added bicarb when I filled the tank with water and the pH did not drop.
And bicarb is also a constituent of Rift Lake salts, which some people make for themselves.
For most fish, having sodium in the water is not good. Apart from the Rift Lakes, very few natural water sources have much sodium in them so fish have not evolved to deal with lots of sodium. This is why bicarb should only used in tanks with Rift Lake cichlids, and during fishless cycling when there are no fish to come to harm.