why is it l'homme rather than le homme?
The H is silent in french and they don't like bumping vowel sounds up next to one another. It sounds off. So for those cases you usually remove the vowel and add an apostrophe. "Ce est" is also like that. It becomes c'est.
How come "est" is not used in this sentence?
French does not have continuous tenses. This is why the English continuous present in the form of "is Verb-ing" has to translate to a French simple present.
Verbs have the 'is' as part of them when translated to the present progressive tense. Mange = eats / is eating