We use 'latter' to talk about the second thing when there are two things. It means the last one we talked about.
I like the first and latter song.
Between tea and coffee, I prefer the latter.
'Latter' means the later part of a time period. It is used to show something happens near the end of a period.
In the latter part of the year, it rained a lot.
The latter half of the movie was exciting.
'Latter' can mean the recent or last period in history or life. It shows something near the end of time or a stage.
In the latter years of her life, she traveled a lot.
The latter era showed many changes.
'Latter' as a noun means the second thing or person mentioned before. It replaces a noun to avoid repeating it.
I like the latter better than the former.
She chose the latter for her project.
'Latter' helps to clearly show which idea or argument is last mentioned. It is useful in discussions or debates.
The latter argument is more convincing.
Between the two ideas, the latter is accepted.