It is difficult to tell if the writer used "cup" in a literal or in a figurative sense. Perhaps it was a literal part of his thank offering to God. On the other hand, the cup may represent his reward in this life, which was physical salvation. Either way he would praise God. Israelites offered votive offerings when God answered their prayers regarding a vow they made. These were peace offerings ( Leviticus 7:16; Leviticus 22:18-23) and public offerings that reminded other worshippers of God"s goodness. The NIV rendering of the end of Psalm 116:14 is probably best. It reads, "...in the presence of all his people."[source]
Think again of Jesus singing Psalm 116:12-14 and raising the cup as He sang. The Jews traditionally sang Psalm 116 after the Passover meal. It is probable that when He sang these verses, He raised the third of four cups of wine the Jews drank at that meal. They called the third cup "the cup of salvation." He knew that that cup would only become a true cup of salvation if He paid His vows to the LORD and proceeded to the cross. [source][source][source]