In order to find the truth let us look at the following passage where the same phrase "gift of the Holy Spirit" is used:
"While Peter was still speaking these words, the Holy Spirit came on all who heard the message. The circumcised believers who had come with Peter were astonished that the gift of the Holy Spirit had been poured out even on Gentiles. For they heard them speaking in tongues and praising God" (Acts 10:44-46).
The Holy Spirit fell on Cornelius and his household and those who had accompanied Peter were astonished that "the gift of the Holy Spirit had been poured out on Gentiles." How did they know that the gift of the Holy Spirit had been poured out on Cornelius and his household?
They knew that they had received the "gift Holy Spirit" because
"they heard them speak with tongues." Let us look at these verses again:
"...the gift of the Holy Spirit had been poured out even on Gentiles. For they heard them speaking in tongues and praising 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 gift of the Holy Spirit had been poured out was because they heard them speak with tongues. So we can understand that the "gift of the Holy Spirit" is the ability to speak in tongues.