Later is an adverb, usually used in relation to time. It means for something to happen in the future. It isn’t define specifically, but just generally in the future.
Note here this can also be used as an exclamation when departing a person or group of people. Later is short for the phrase see you later. Outside the United States, the plural laters is more common.
Latter is an adjective to describe one of two things in a comparison. The latter happens or exists after something else; or toward the end of something, as opposed to the beginning.
These words are similar but not synonyms or interchangeable. It is helpful to remember that later deals in time and latter deals in space or sequence.
Side note: ladder is a common misspelling of latter. A ladder is something that one climbs to be able to reach tall heights. The confusion is most prevalent if someone has never seen latter spelled and simply spells based on enunciation, which can change based on accents and culture.
Examples
The teenager remained surprisingly calm as the Brit-winner joined her on stage and later explained: “I didn’t want to stop, but I wanted to talk to him.” [BBC News]
Worse, said Paul Doghramji, a family physician in Collegeville, Pa., who has conducted research on gout, people who suffer from gout are more prone to heart attack, stroke, kidney damage, premature arthritis, diabetes and sleep apnea (the latter because many people with gout are also obese). [The Washington Post]