The word science literally translates to “knowledge”; however, if you are asking what science is then we have to say it is a methodology used to investigate and observe the physical world. This methodology incorporates such things as trial and error, elimination, observation, consensus building, peer review and falsification; it also makes extensive use of philosophical tools like logic and critical thinking.
Science is important because it the only trustworthy means of investigating the physical world that humanity possesses; that is, science does not stand or die on unsubstantiated claims to knowledge like pseudoscience such as acupuncture (use needles to change your ‘chi’), homeopathy (water has memory and ‘like cures like’), or astrology (your fate is somehow connected to the stars). Rather, scientific claims are tested and either proven true or false, i.e. unlike pseudoscience, you do not believe in science—if you ignore the existence of gravity walking out of a window of a tall building gravity will still apply to you; thus, we accept or reject scientific theories on the basis of the prevailing evidence.
Science is likewise important because it provides people with actionable knowledge; that is, you can reliably plan for the future and make predictions based on scientific theories and models. Also, scientific literacy can help protect you from being exploited by peddlers of woo and adherents of pseudoscience.