The "First Invitation" refers to the early period of the LDS Church from 1830 to the martyrdom of the Prophet Joseph Smith. It probably also includes the period of the subsequent various splinter groups which formed, especially the large Utah church which has had a major missionary program inviting all to accept the restored gospel of Jesus Christ.
The "Second Invitation" refers to the current period of time, beginning with the call of Mauricio A. Berger in Brazil to begin what could be called the "Rebirth of the LDS Church". All of the various splinter groups of the original church founded by Joseph have gotten off track from the restored gospel, each losing various parts of the gospel the priesthood, and changing ordinances.
The first big step to begin the Second Invitation was for Mauricio to translate the first few plates of the sealed portion of the same Plates of Mormon from which Joseph Smith had translated the Book of Mormon. They had been delivered to him by the Angel Moroni, along with the interpreting stones. It was published to become The Sealed Book of Mormon in March 2019.
Then a branch of the Church was formed first in Missouri in April 2019, and later in Utah in April 2020. This website represents the branches of the western USA, beginning in Duchesne, Utah.