"Yes, the man is calm."
Translation:Oui, l'homme est calme.
"Le homme" is improper French.
"Le" is pronounced [luh] and the first sound in "homme" is [o]. The vowel sound conflict between [uh] and [o] is avoided by eliding (remove the vowel and replace it with an apostrophe) the article.
The same applies to "la", with "l'eau" instead of "la eau".
Elisions are used with a number of little words: je, ne, me, de, le, la, te, se, que
Because it's just easier to say l'homme that le homme, it's a slang. I guess like we use all those apostrophes in English also; it makes the spoken language to flow faster. Don't you think so? We have many words like that in Spanish also, we constantly shorten "para qué?" To "pa'que" although we would never write it like that unless we're speaking with a very familiar person. L'homme just flows better ;)
"La" is the feminine singular definite article. So it cannot introduce a masculine noun. In addition, "homme" starts with a vowel sound (o) because the H is mute. So the masculine article "le" must be elided (drop the vowel and replace it with an apostrophe) to ease pronunciation: l'homme.