Leviticus 23:9-21: And the LORD spake unto Moses, saying, Speak unto the children of Israel, and say unto them, When ye be come into the land which I give unto you, and shall reap the harvest thereof, then ye shall bring a sheaf of the firstfruits of your harvest unto the priest: And he shall wave the sheaf before the LORD, to be accepted for you: on the morrow after the sabbath the priest shall wave it. And ye shall offer that day when ye wave the sheaf an he lamb without blemish of the first year for a burnt offering unto the LORD. And the meat offering thereof shall be two tenth deals of fine flour mingled with oil, an offering made by fire unto the LORD for a sweet savour: and the drink offering thereof shall be of wine, the fourth part of an hin. And ye shall eat neither bread, nor parched corn, nor green ears, until the selfsame day that ye have brought an offering unto your God: it shall be a statute for ever throughout your generations in all your dwellings.
          And ye shall count unto you from the morrow after the sabbath, from the day that ye brought the sheaf of the wave offering; seven sabbaths shall be complete: Even unto the morrow after the seventh sabbath shall ye number fifty days; and ye shall offer a new meat offering unto the LORD. Ye shall bring out of your habitations two wave loaves of two tenth deals: they shall be of fine flour; they shall be baken with leaven; they are the firstfruits unto the LORD. And ye shall offer with the bread seven lambs without blemish of the first year, and one young bullock, and two rams: they shall be for a burnt offering unto the LORD, with their meat offering, and their drink offerings, even an offering made by fire, of sweet savour unto the LORD. Then ye shall sacrifice one kid of the goats for a sin offering, and two lambs of the first year for a sacrifice of peace offerings. And the priest shall wave them with the bread of the firstfruits for a wave offering before the LORD, with the two lambs: they shall be holy to the LORD for the priest. And ye shall proclaim on the selfsame day, that it may be an holy convocation unto you: ye shall do no servile work therein: it shall be a statute for ever in all your dwellings throughout your generations.

Numbers 28:26 - 31: Also in the day of the firstfruits, when ye bring a new meat offering unto the LORD, after your weeks be out, ye shall have an holy convocation; ye shall do no servile work: But ye shall offer the burnt offering for a sweet savour unto the LORD; two young bullocks, one ram, seven lambs of the first year; And their meat offering of flour mingled with oil, three tenth deals unto one bullock, two tenth deals unto one ram, A several tenth deal unto one lamb, throughout the seven lambs; And one kid of the goats, to make an atonement for you. Ye shall offer them beside the continual burnt offering, and his meat offering, (they shall be unto you without blemish) and their drink offerings.

This festival commemorates the giving of the Torah on Mt Sinai seven weeks after the beginning of the Passover. When Moses received the Torah, the Israelites entered into a covenant with God be declaring (Exodus 19:8). With that act, the Israelites completed the process of liberation from bondage in Egypt be freely accepting responsibility to uphold the laws of the Torah.

From the LDS BIBLE DICTIONARY - FEASTS
Fifty days (Leviticus 23: 16) after the Feast of the Passover, the Feast of Pentecost was kept. During those 50 days the harvest of corn was being gathered in. It is called (Exodus 23: 16) "the feast of harvest, the firstfruits of thy labours" and (Deuteronomy 16: 10) "the feast of weeks." The feast lasted a single day, which was a day of holy convocation (Leviticus 23:21); and the characteristic rite was the new meal offering, that is, two loaves of leavened bread made of fine flour of new wheat. Special animal sacrifices were also made (Leviticus 23: 18) and freewill offerings (Deuteronomy 16: 10). The festival was prolonged in later times, and huge numbers of Jews attended it. Of this the narrative in Acts 2 is sufficient proof.

From EASTON'S BIBLE DICTIONARY - PENTECOST
Pentecost - i.e., "fiftieth", found only in the New Testament (Acts 2:1; 20:16; 1 Corinthians 16:8). The festival so named is first spoken of in Exodus 23:16 as "the feast of harvest," and again in Exodus 34:22 as "the day of the firstfruits" (Numbers 28:26). From the sixteenth of the month of Nisan (the second day of the Passover), seven complete weeks, i.e., forty-nine days, were to be reckoned, and this feast was held on the fiftieth day. The manner in which it was to be kept is described in Leviticus 23:15-19; Numbers 28:27-29. Besides the sacrifices prescribed for the occasion, every one was to bring to the Lord his "tribute of a free-will offering" (Deuternomoy 16:9-11). The purpose of this feast was to commemorate the completion of the grain harvest. Its distinguishing feature was the offering of "two leavened loaves" made from the new corn of the completed harvest, which, with two lambs, were waved before the Lord as a thank offering.
The day of Pentecost is noted in the Christian Church as the day on which the Spirit descended upon the apostles, and on which, under Peter's preaching, so many thousands were converted in Jerusalem (Acts 2).