During Kol Nidrei we traditionally hold at least two Sifrei Torah, Torah scrolls.
Many congregations have transformed this into conferring the honor of holding Sifrei Torah to the distinguished and respected members of the community. It is a blessing to have many scrolls, and that is displayed by honoring individuals with holding them.
The scrolls are held during the chanting of Kol Nidrei thrice through. As you may have noticed, the covers of each Sefer Torah and of each shulhan (reading table) are changed to white for the period between Rosh Hashanah and Simhat Torah.
Different congregations confer different honors on their distinguished and respected members. We are not certain which came first, conferring this honor on past Beth Shalom presidents or having a Torah cover made with each president’s name at the end of his/her term, but we have the white covers for the past presidents, and it is a nice honor for the congregation to show continuing respect after their terms of office have expired.
Other synagogues have different traditions. There are some who (in a more mercenary vein) auction off the honor - there are even online auctions - to the highest donors specifically for that honor. The first scroll taken out is called the Sefer Kol Nidrei, and often draws the highest bids.
Some synagogues offer their board members the honor, and give other honors to past presidents. There are numerous honors conferred during the High Holy Days, including opening and closing the ark, doing readings, reading Torah, chanting haftarah, aliyot, blowing shofar, and more.
Carrying a Sefer Torah in a procession is called “hakafah,” The plural is “hakafot,” which is what we saw on Yom Kippur at Kol Nidrei, and will see again large on Simhat Torah. In fact, we see hakafah every time we take out and return the Torah!
Thank you very much for asking this question.