The principle of remembering does well for the individual just as it does for the nation, as one commits oneself through the covenant of the Gospel. One of my favorite analogies regarding remembering and covenants comes, light-heartedly enough, from Seinfield.
Making Covenants is not important in and of itself; it is the remembering and keeping of them that truly matter. Thus, after making the initial covenants, we are to remember them after we make them.
The Day of Atonement shortly follows the feast of trumpets, signifying a purification and readiness once the call has been made. following that, an even greater outpouring of light and water are promised through the Feast of Tabernacles. I have found great strength in studying the New Testament this year and recognizing the format, or conditions of the covenants, as well as the promised blessings of them. For example, the discussion of Jesus with Nicodemus at the beginning of His ministry included a discussion of being born of water and the Spirit, which has many connotations, including baptism of water and the gift of the Holy Ghost, as well as a recognition of following both the conditional elements of the covenants (the requirements) as well as not simply completing them in form only, but truly allowing the ordinance with its accompanying covenants to change the individual, or to become. It is no small significance that at the end of His ministry, he is reiterating similar principles in the Feast of Tabernacles with His I AM statements of being the Light and the Water (as well as the Bread, the True Vine, and so one). John 7:37 references the Last Great Day, but whether this refers to the Feast mentioned, or simply the last day of the Prior feast is unknown to me at this time. It shows a completeness and fulfilling of covenants when Jesus asks them to come unto Him and partake of a lasting Peace, rather than anything temporal, and this is what we are asked to do as well as we prepare for our own "Last Great Day".
Hanukkah is a sacred Feast day as well, and in my mind associated with a redeemed state, or one that is completed after a final battle. Similar to the feelings of rejoicing after all enemies are conquered, Death being the final one, this Feast recognizes a redemption through action and covenants as well as faith in a Redeemer.
Purim to me signifies a complete freedom from governments, kingdoms, and other entities that will occur when One comes to govern over all the earth in wholeness and Fulness. Similar to the prior Feast, redemption is at hand, and rejoicing in being able to to governed in purity.
James E Faust, another modern apostle, elucidates on counsel from Joseph Smith regarding being Born Again in this way:
Feel free to share your insights, approaches, and understanding in the comments below.