The context in Psalm 68:18 is the exodus from Egypt. The Israelites escaped from Egypt, and plundered the Egyptians. The Lord is the one who delivered them from Egypt "with an outstretched arm."
The same passage is used in the New Testament. After his death, the humanity of the Second Person of the Godhead entered Sheol. His humanity led captivity captive, since Sheol was the staging point for Old Testament saints who died before the resurrection of Jesus Christ. That is, while believers in the Old Testament had righteousness, they did not have the free gift of eternal life, which was promised in the New Covenant. Therefore they "rested" in a confined location called Sheol until the resurrection of Jesus Christ, who led them out of Sheol.
Please notice that the same days of Nisan in the first month of the Hebrew calendar correspond exactly to the dates of the crucifixion and resurrection of Jesus Christ. That is, on the 16th of Nisan was the date when the Israelites escaped from Egypt and the next morning (Sunday) was when the waters wiped out the Egyptian Army. In like fashion, Jesus is the Second Moses (the "prophet" in Acts 3:20-22), who delivered the Old Testament believers from Sheol. His resurrection was the "water" that wiped out death and its power.
I will translate this to English later, but here is a preview.
In the Old Testament, the plunder from the Egyptians was material -- gold, earrings, and the like, and the Jews received the Law at Sinai fifty days later. They dedicated their plunder to God in Exodus 25:1-9, when God gave them the Law. In the New Testament, the plunder is spiritual power, since Satan has been plundered (like the Egyptians). Satan's power was wiped out by the "water" of eternal life at the resurrection. Our plunder is the spiritual power which we receive as spiritual gifts, which are distributed to us by the Holy Spirit.
The parallels in regard to Psalm 66:18 to Ephesians 4:8-10 (not to mention Romans 10:7) are very striking and very impressionable. For example, Sinai is mentioned in Psalm 66:17, since the Jews received the Law at Sinai, when their plunder was dedicated to God (Exodus 25:1-9). The distribution of spiritual gifts happened at Pentecost, which was the exact same day that the Law was given at Sinai. Again, I am sorry that this is not in English, but you will see how the remarkable coincidence of these dates and events.
Pentecost ("Pfingsten" in German) and Shavuot ("Schawuot" in German) are the exact same dates on the calendar. In other words, the Old Covenant and the New Covenant were announced to the nation of Israel on the very same date --> exactly 50 days after the "escape" from Egypt (and Sheol), when plunder was seized from the enemy. The dates correspond (in both cases) to the time when the plunder was then received by God and distributed to God's people as his temple (sanctuary). We are the sanctuaries of the Holy Spirit in the New Testament. We therefore have the plunder of spiritual power because the Second Moses ("Prophet" in Acts 3:20-22) delivered the captives, and as a result plunder was delivered in the Covenant of God to the people: in the New Covenant, this plunder is spiritual power, since we are the sanctuaries of God (please see Exodus 25:8-9).
Do you see the parallels?