On the day of Pentecost the believers received a gift bestowed by the Holy Spirit:
"Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Spirit" (Acts 2:38).
Peter said that what happened to Cornelius was the same thing that happened on the day of Pentecost. Now let us look at the actual events when Cornelius received the "gift of the Holy Spirit":
"While Peter yet spake these words, the Holy Spirit fell on all them which heard the word. And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Spirit. For they heard them speak with tongues, and magnify God" (Acts 10:44-46).
The Holy Spirit fell on Cornelius and his household and those who had accompanied Peter were astonished
"because that on the Gentiles was poured out the gift of the Holy Spirit." How did they know that the gift of the Holy Spirit had been poured out on Cornelius and his household?
They knew that the Holy Spirit had been poured out on them because "they heard them speak with tongues." Let us look at these verses again:
"...because that on the Gentiles also was poured out the gift of the Holy Spirit. For they heard them speak with tongues, and magnify God..."
Here the word "for" is translated from the Greek word
gar, and the meaning of that word as used here is
"it addresses the Cause or gives the Reason of a preceding statement or opinion" (Thayer's Greek-English Lexicon).
The reason that those with Peter knew that the Holy Spirit was poured out on Cornelius and his household was because they heard them speak with tongues.
This "gift" of being able to speak in tongues is spoken of here by Paul where he names many of the gifts "given by the Spirit":
"Now there are diversities of gifts, but the same Spirit...For to one is given by the Spirit the word of wisdom; to another the word of knowledge by the same Spirit; To another faith by the same Spirit; to another the gifts of healing by the same Spirit; To another the working of miracles; to another prophecy; to another discerning of spirits; to another divers kinds of tongues; to another the interpretation of tongues" (1 Cor.12:4,8-10).