What are pentecostal missions?

Pentecost comes from a Greek word that means fiftieth. In the Bible, after the death of Jesus and his resurrection, as described in the New Testament book of Acts, Jesus told his disciples to wait for the Holy Spirit to descend on them, and that they would be given power to witness and be instruments of signs and wonders at that time. Here is the scriptural reference from the NIV version of the Holy Bible:

But you will receive power when the Holy Spirit comes on you; and you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth. (Acts 1:8)

This is what the disciples and apostles were waiting for when the events of Acts 2:4 take place. The book of Acts says that 120 were waiting in the room where they were staying, praying constantly. On the day of Pentecost, the fiftieth day after Passover in Jewish culture (also known as the Feast of Weeks) and the fiftieth day after Easter in Christianity, these events are recorded in scripture:

When the day of Pentecost came, they were all together in one place. Suddenly, a sound like the blowing of a violent wind came from heaven and filled the whole house where they were sitting. They saw what seemed to be tongues of fire that separated and came to rest on each of them. All of them were filled with the Holy Spirit and began to speak in other tongues as the Spirit gave enabled them. (Acts 2:1-4 NIV)

There is a denomination (several, actually) within Christianity called Pentecostals. They see these verses in Acts as foundational to their faith. They place a high emphasis on the work of the Holy Spirit, the gifts of the Holy Spirit (described in the book of Corinthians) Many pentecostalists believe in a second baptism, known as the baptism of the Holy Spirit. They believe that the evidence of being baptized in the Holy Spirit is the ability to speak in tongues.
Pentecostalists who go on missions will spread the message of the Gospel just like other denominations of Christianity. The difference being they will likely speak in tongues, encourage the baptism of the Holy Spirit, and seek to have in operation the gifts of the Holy Spirit such as word of knowledge, word of wisdom, gifts of healing, prophecy, the discerning of spirits, speaking in tongues, and the interpretation of tongues. All these gifts are described in 1st Corinthians 12:8.