In many words the letter e is potentially silent, a characteristic which has three French names: e caduc, e instable, and e muet. Though e muet is the most common term, e instable is the most accurate.
Pronoun usage and pronunciation varies greatly between formal and informal French. Much of what you learn at school is formal and doesn't reflect how French is actually spoken. If you want to sound more French in informal situations—not to mention understand what you hear—you need to be aware of these pronoun differences.
Some liaisons in front of a vowel or h muet are optional, which means it up to you to decide whether to pronounce them. However, that decision matters: more liaisons means more formal speech, so obviously fewer liaisons means more informal, possibly even familiar speech.
Think you've mastered French pronunciation? See how well you can twist your tongue around some virelangues. Repeat these alliterative and/or rhyming and/or confusing phrases as quickly as possible to put your French pronunciation to a test that even native speakers have trouble with.