The word means an upper room or the upper part of the house. [5253 - huperoon].
If there is any significance beyond being the highest part of the house, it would be found in who typically resided there. According to Thayer's Lexicon the upper room was where the women resided. [Thayer's]
Should that be the case, the early church met in the part of the house usually occupied by the women:
And when they had entered, they went up into the upper room where they were staying: Peter, James, John, and Andrew; Philip and Thomas; Bartholomew and Matthew; James the son of Alphaeus and Simon the Zealot; and Judas the son of James. These all continued with one accord in prayer and supplication, with the women and Mary the mother of Jesus, and with His brothers. (Acts 1:13-14 NKJV)
The believers stayed together in the upper room where they collectively prayed and made supplication; essentially this would be the first "church service."
The disciples were from Galilee and would need a place in Jerusalem to stay while they waited as Jesus had instructed them:
And being assembled together with them, He commanded them not to depart from Jerusalem, but to wait for the Promise of the Father, “which,” He said, “you have heard from Me; for John truly baptized with water, but you shall be baptized with the Holy Spirit not many days from now.” (Acts 1:4-5 NKJV)
This would lead to an interesting parallel found in Acts 16, when Paul brought the Gospel to Macedonia:
And when she and her household were baptized, she begged us, saying, “If you have judged me to be faithful to the Lord, come to my house and stay.” So she persuaded us. (Acts 16:15 NKJV)
In both cases the apostles made their temporary residence in the place where a woman stayed. In Jerusalem it was the upper part of the house; in Philippi it was the entire house.