Context
In Deuteronomy 16, the feast laws regulate how Israel is to gather before the Lord in the place He chooses. Verse 16 belongs to that larger pattern of appointed assembly, rejoicing, remembrance, and covenant allegiance.
Common Interpretations
A common reading of this section is that one obligation of worship under the old covenant was gathering before God at the appointed place and time. The emphasis is not private spirituality detached from assembly, but covenantal appearing before the Lord. Interpreters also note that no one was to appear empty-handed. The gathering itself carried the expectation of responsive offering and allegiance before God.
Current Position
This site's current position is that passages like Deuteronomy 16 matter because they show worship in Scripture has always included gathered, ordered, God-directed assembly. Private devotion has its place, but it is not a replacement for appearing before the Lord with His people. The old-covenant feast structure is not carried over unchanged into the ekklesia, but the underlying pattern still cuts against the modern reduction of worship to private feeling or passive attendance.