Wearing the hijab is important in ISLAM because it is an act of obedience. It is a sign of obeying Allah ta’ala and his prophet Muhammad, peace be upon him. Allah ta’ala says:
And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their head covers over their chests and not expose their adornment except to their husbands, their fathers, … [24:31]
Also, Allah ta’ala says:
O Prophet! Tell your wives and daughters and the women of the believers to draw their cloaks close round them (when they go abroad). That will be better, so that they may be recognized and not annoyed. Allah is ever Forgiving, Merciful. [33:59]
So, when a woman wears a hijab, she shows that she cares to obey her Creator and her Prophet.
Also, the way you dress affects your personality. If you dress like a king, it’s hard to be humble. If you dress like a beggar, you can’t act proud. If you dress like a muslim woman, automatically you’ll try to act like a pious muslim woman.
When a woman hides her beauty from unrelated men, she protects herself from lustful gazes and helps to save men from sinful thoughts as well. It is true that even women who dress modestly sometimes get lustful looks; but when a woman covers herself properly, she is less likely to attract lustful looks than others who don’t.