More formally written, sun’s out, guns out—this phrase means “when the weather is sunny, it is time to wear a shirt that shows your upper arm muscles (biceps).”
When the weather is sunny, we say “the sun is out.” Also, when you can see the moon or stars, you say “the moon is out” or “the stars are out.” Strangely, you wouldn’t use the word in for the opposite meaning; for example, if the weather is cloudy, you wouldn’t say the sun, moon, or stars are “not out.”
Guns are American slang for biceps—upper-arm muscles. Probably because some men feel powerful if they have big arm muscles and American culture tends to illustrate power in terms of guns and violence (particularly in movies and video games). And such men feel that it is good to show off their muscles—just as some American men like to show off their actual guns. A shirt with no sleeves—technically a tank-top—is also called a muscle-shirt. So, when people say suns out, guns out, they mean “if the weather is nice, it is time to wear a shirt that shows your arm muscles.”