Yes, Boys State holds alot of weight in the application process. It's on all three SA's Class Portrait, right next to honor society, varsity athletics, and Eagle Scout.... It has its own check-box on the application. I read somewhere that West Point values Boys State as much as Eagle Scout.
I went to Boys State last summer and had a blast. It's typically a one week long seminar where you attend different mock conventions and run for government office for your "Boys State" (i.e. governor, senator, house rep, commisioner, judge, etc...). You give speeches, vote on fake legislation, and determine laws and rules for your Boys State. And most importantly, you make tons of friends with like-minded individuals who have the same life ambitions. In fact, a few people I met at Boys State I met again at summer seminar. It's definitely worth your time.