When you imply, you hint at something rather than saying it directly. Imply comes from an Old French word that meant “to enfold.” You can think of an implied statement as hidden or folded into what was actually said. For example, a writer can imply that a character is the murderer without saying it directly.
Writers or speakers imply. Listeners or readers infer.
When you infer, you deduce some meaning that was left unsaid. Infer comes from a Latin word that means “to bring in.” You can think of readers or listeners using their own interpretation to bring a meaning that isn’t explicitly stated into a sentence. For example, a reader who sees that a character has motive and opportunity may infer that the character is the murderer.
The incorrect use of infer to mean imply is so common that in a decade or so it may be considered standard, but for now, careful writers and speakers continue to make a distinction.
But the fact that some geniuses were laughed at does not imply that all who are laughed at are geniuses. They laughed at Columbus, they laughed at Fulton, they laughed at the Wright brothers. But they also laughed at Bozo the Clown. — Carl Sagan
I would not wish to imply that most industrial accidents are due to intemperance. But, certainly, temperance has never failed to reduce their number. — William Lyon Mackenzie King
From a drop of water a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other. — Arthur Conan Doyle
We infer the spirit of the nation in great measure from the language, which is a sort of monument, to which each forcible individual in a course of many hundred years has contributed a stone. — Ralph Waldo Emerson(Please retain the reference in reprint: http://www.letpub.com/author_education_imply_versus_infer)