#V_i# is the velocity of the object at that instant or instantaneous velocity.
#lim t to 0# states that the time we are observing the velocity is limited, and is now so short, that it is approaching #0.000000 sec#
#((triangled)/(trianglet))# informs us that the velocity is a function of the distance divided by the time, and since we are considering velocity here the direction must also be defined.
The #triangle'#s tell us the function refers to the change in something, in this case the change in distance divided by the change in time.
As you might suspect, since the #trianglet# observing time is so short, the #triangled# distance travelled will also be short compared to the overall distance travelled. As a result, we can be sure that the calculation of the instantaneous velocity will be correct for the moving object, which may be either accelerating, decelerating, or moving at a constant velocity.
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