"latter day", when referring to religious and Biblical things, generally means "last day" or "end time", referring to the years leading up to the return of Jesus Christ. In other uses (and occasionally in a religious context), it could refer to the most recent day, or the modern day.
Latter Day (Saints)
To "simplify an expression" is simply to make it as simple as possible. Ex: 2+2 simplified would be 4. an easy way of thinking about it is removing as many numbers and symbols as possible without changing the expression's meaning. There are also several standards that are universally accepted. Take x*2 for example. this is never seen in an expression this way, but instead as 2x. it is the same thing, but the latter is the accepted version.
Latter-day Dissent was created in 2011.
Latter-day Trumpet was created in 2003.
Latter-Day Pamphlets was created in 1850.
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Apostle - Latter Day Saints - was created in 1830.
Stake - Latter Day Saints - was created in 1834.
Teacher - Latter Day Saints - was created in 1830.
The Story of the Latter-day Saints was created in 1992.
Priest - Latter Day Saints - was created in 1830.
Latter Day Church of Christ was created in 1977.