From the second night of Pesach, we count the Omer - counting off the days for seven weeks until Shavuot. Counting is an expression of anticipation. Grown-ups count the weeks until the next holiday; kids count the minutes until the end of class. It is also implies a sense of progress and direction.
Saying that today is the third day of the Omer requires knowing that yesterday was the second and tomorrow is the fourth - where we have come from and where we are going towards. So counting the days from Pesach teaches that it is connected to and completed by Shavuot.
The Exodus from Egypt was not a self-sufficient event. It was a first step towards Sinai, receiving the Torah and becoming a people with a mission. Freedom without a purpose is merely free to kill time. The kabbalists teach that every day of the Omer is a chance to reflect on and purify a different spiritual trait, and so to shed the vestiges of slavery and become worthy to renew our purpose.