What does “b” mean in an equation of the regression slope Y=a+b*X?

Yes. You can also understand it this way: 1 unit increase in X is associated with b unit increase (or decrease) in Y.

I see.

“b” is the estimated parameter that signifies the corresponding change in y when one unit change happens in x. In this way, it represents the degree to which the line slopes upwards or downwards.