Let's have a listen to Cali's beautiful tune C'est quand le bonheur, paying special attention to this line:
Il paraît que vous faiblissez devant les hommes bien habillés
It appears that you swoon for well-dressed men
Caption 21, Cali: C'est quand le bonheur
Do you hear a "z" sound sneaking its way in between les and hommes, such that we hear “les-Zhommes”? You might also notice an "n" sound between bien and habillés, such that we hear “bien-Nhabillés."
What you are hearing are examples of liaison, which often happens when the (usually silent) final consonant of one word can be heard pronounced at the beginning of the following word, if the following word begins with a vowel or a mute h (learn more about the distinction between “mute h” and “aspirated h” here).
In most cases, the sound produced by liaison is very straightforward. In the Cali song, for example, the n of bien tacks right onto habillés. Simple! As is the first liaison we hear in the next line of the song:
Je suis tendu, c'est aujourd'hui que je viens vous offrir ma vie
I am tense, today is the day I am coming to offer you my life
Caption 22, Cali: C'est quand le bonheur
We hear a liaison in "c’est-Taujourd’hui." The final consonant of c'est, t (which we usually don't hear in French), binds with the vowel sound at the beginning of aujourd'hui.
But liaison doesn't always result in the sound you might expect. The next liaison in the line is in vous offrir. As in the case of les hommes, we have a preceding word that ends in an s (generally not pronounced in French) rendering a "z" sound that binds to the next "vowel-starting" word, resulting in "vous-Zoffrir."
A final s is not the only consonant that renders a "z" sound in liaison; the same is true for a word ending in -x. Let’s return to Cali and his romantic vieux amants (with our handkerchiefs close by):
Car qui mieux que ces vieux amants sait qu'on perd l'amour..
Because who knows better than those old lovers that we lose love...
Caption 34, Cali: C'est quand le bonheur
As you can hear, Cali is singing of "vieux-Zamants"; the final x in vieux, usually silent, renders a "z" sound at the beginning of amants.
Another case where a consonant produces an unexpected sound in liaison involves words ending in -d. Here, the liaison carries over not as a "d" sound, but a "t" sound.
Here's an example concerning Viktor Bout, a notorious arms dealer who was the basis for Nicolas Cage's character in the movie Lord of War:
L'un des hommes les plus recherchés au monde, finalement arrêté dans un grand hôtel de Bangkok...
One of the most sought after men in the world, finally arrested in a big hotel in Bangkok...
Caption 5-6, Le Journal: Viktor Bout
Did you catch where Bout was arrested? Not in a "grand-Dhôtel," but a "grand-Thôtel."
As you expose yourself to more authentic French, you will become accustomed to liaison and start to get a feel for where it does, and doesn't, belong. It's a tough subject to get a full handle on, and it's not uncommon to hear native French speakers adding a liaison where it "technically" shouldn't exist, or vice versa.
Here is an interesting article on liaison from french.about.com:
And another, from the Académie Française: