Learn Italian: È un'idea molto importante. - It is a very important idea.

Because idea is a feminine noun that starts with a vowel. When the feminine article una is followed by a vowel, it drops its final -a to make pronunciation smoother and replaces it with an apostrophe, becoming un'.

Do masculine words starting with a vowel also use un' with an apostrophe?

No, they don't. Masculine words starting with a vowel just use the normal masculine article un with no apostrophe (like un amico). The apostrophe is actually a helpful clue that the noun you are looking at is feminine!

Idea is a feminine noun, so why doesn't importante end in -a?

Importante belongs to a specific group of adjectives that always end in -e in the singular. They use this exact same -e ending for both masculine and feminine nouns, so it doesn't change to match the gender of idea.

Why is the word order idea molto importante and not molto importante idea?

In Italian, descriptive adjectives like importante usually go after the noun they describe. The word molto (very) has to stick directly to the adjective it modifies, so the entire chunk molto importante is placed after the noun.