Pronunciation is really important. Much more important than grammar. For example, when you’re speaking, if you use a present tense verb instead of a past tense verb, it probably won't affect your overall message. But if your pronunciation isn’t comprehensible, you’re in trouble... no matter how perfect your grammar is.
So, what can you do to improve your pronunciation? The most important thing to understand is that English is a stress-timed language. English pronunciation focuses on specific stressed words while quickly gliding over other non-stressed words. Stressed words include nouns (“dog, table”, etc.), verbs (“sit, run”, etc.), adjectives (“beautiful, wonderful”, etc.) and adverbs (“quickly, slowly”, etc.). Most of the other words are not stressed and include determiners (“a/the”), auxiliary and modal verbs (“am, is, have, can”, etc.) prepositions (“in, at, to”, etc.) conjunctions (“but, and”, etc.) and pronouns (“he, she, they”, etc.).