During the seven weeks from the second night of Pesach until Shavuot, we count the Omer. In ancient times, the Omer represented the first sheaf of the harvest that God instructed the Israelites to bring to the priest (Leviticus 23). The Israelites were then to count fifty days between the bringing of the omer and the bringing of a second offering of new grain. The omer also helps us to make a connection between Pesach, when we were liberated from bondage, and Shavuot, when we received the Torah.
In early Rabbinic times, the omer took on additional significance as a period of mourning: our tradition teaches that twelve thousand of Rabbi Akiva's disciples died between Pesach and Shavuot. Our rabbis teach that these disciples of Rabbi Akiva were afflicted by a deadly plague because they did not respect one another; historians ascribe their deaths to the Hadrianic persecutions following the Bar Kochba revolt. Some engage in some mourning practices either throughout the Omer or until Lag Ba'omer: these include refraining from haircuts, scheduling weddings, and holding celebrations with live music and dancing.
We count the Omer each night after dark with a blessing. One who forgets to count at night may count in the morning; the counting in the morning is traditionally done without a blessing. The Omer is counted during the Ma'ariv service before Aleinu and can be found in Mishkan T'filah on page 570.