Omer is counted for 49 days, from the second day of Passover to the day before Shavuot.  Omer connects the two holidays both physically and spiritually.  In Biblical times, an omer (a specific measure of volume) of barley was brought as an offering to the Temple in Jerusalem on the second day of Passover.  Once the barley offering had been brought, all grain changed status from “chadash” to “yashan” and could be eaten.
Due to tragedies that occurred during the omer period, especially the death of 24,000 students of Rabbi Akiva during the second century, we observe a semi-mourning period during 33 days of the 49 days of the omer.