The slope of the secant line is the average speed between the starting and ending point; remember the units on the ordinate are distance units and on the abscissa are time units; therefore the units of the slope are speed units, i.e. distance units/times units.
The tangent can be visualized as the limit of the average speed as the time difference becomes smaller and smaller; thus the slope of the tangent is instantaneous speed. In math terms this limit is called the derivative of the distance function.
Note: I have used the word speed rather than velocity, because velocity is a vector quantity, i.e. it has a magnitude (speed) and a direction.
