This wasn't easy regarding "What's a Pentecost".
I think the biggest reason is that it bridged time and events that tied the Jews into the modern Christian church. So some information I found was specific to the Old Testament Feast of Weeks/Harvest (see Exod 34:22,/23:16) and the Day of First Fruits (Num 28:26) which fell on the 50th day after the feast of the Passover. While other information was specific to the events in the book of Acts (coming of the Holy Spirit) which transformed the Jewish Festival into a Christian anniversary.
Anyway.... here are some definitions from my friends at Dictionary.com
Pen·te·cost (pěn'tĭ-kôst', -kŏst')
Easton's 1897 Bible Dictionary
Pentecost i.e., "fiftieth", found only in the New Testament (Acts 2:1; 20:16; 1 Cor. 16:8). The festival so named is first spoken of in Ex. 23:16 as "the feast of harvest," and again in Ex. 34:22 as "the day of the firstfruits" (Num. 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 Lev. 23:15-19; Num. 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" (Deut. 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).
American Heritage New Dictionary of Cultural Literacy, Third Edition - Pentecost
In the New Testament, the day that the Holy Spirit descended upon the disciples of Jesus. Pentecost is the Greek name for Shavuot, the spring harvest festival of the Israelites, which was going on when the Holy Spirit came. The disciples were together in Jerusalem after Jesus' Resurrection and return to heaven, fearful because he had left them. On that morning, however, “there appeared unto them cloven tongues like as of fire, and it sat upon each of them. And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance.” Because of the festival, crowds of visitors were in Jerusalem, speaking many languages, but the disciples of Jesus moved among them and spoke to them all, and “every man heard them speak in his own language” about “the wonderful works of God.” Peter then made a powerful speech to the crowds in the city, and many were baptized as new followers of Jesus.
