The expression literally means, "Be men," or "Be manly." Paul uses the Greek verb andrizomai in the middle voice. It's another one-word imperative, though it's hard to make it one word in English. It means "play the man."
It's a word that speaks of masculinity as opposed to femininity. He's not saying be grownups rather than children; he's saying, "Act like men, not like girls." And frankly, that was a fitting charge to give to the church at Corinth. As a reminder and a rebuke, it is also well-suited for a large segment of evangelicals today.
Remember, the context is militant. This is first of all a call to arms and a summons to battle. "Fight like men; defend the faith in a manly way." That is surely the cardinal idea here.
Now it's worth noting that this verse is written to the whole church—it's not addressed to men only—and much less does Paul single out only the elders and the church leaders. This apples to every Christian. But while this applies to everyone in the church, it is nevertheless the particular duty of the elders and pastor to model the spirit of virile, vigorous, vigilant faith—steadfast and courageous. And I love it that Paul has no scruples about connecting those ideas with manliness. "Act like men!" Masculinity. That is certainly one of the missing qualities of churches today.
In my judgment, the typical evangelical church of this generation has become weak and womanly. Churchgoers demand that preachers be soft and dainty—especially when they are dealing with hard-edged truths. If you don't sufficiently tone down every severe text or hard-to-receive doctrine in the Bible, the tone police will write you up for an infraction before you can get from the pulpit to the front door. All the rough edges of every truth must be carefully sanded smooth and painted in pastel tones. We've traded up to cushy seats instead of hard-bench pews and we expect our preachers to fashion their message accordingly. None of this sinners-in-the-hands-of-an-angry-God stuff.
Instead, today's evangelicals favor feminine themes: Let's talk about our emotional hurts, our personal relationships, our felt needs. We're hurting people. The church has begun to look weak, effeminate, frightened, sissified—like a society of fops and milksops instead of soldiers.
These trends have received a lot of attention in recent years, and more and more people are recognizing the problem. The church is not reaching and ministering to men—we're actually driving them away. But those who see the problem more often than not have really bad solutions. You know: have the Men's Bible studies over beer, cigars, and poker games. Get your men watching cage-fighting and encourage them to develop a taste for blood sport. Or go out in the woods, put on war paint, and perfect the art of the primal scream. Salt your vocabulary with a sailor's favorite expletives. Or (my favorite) Live Action Role Playing, or LARPing, where you dress up like a knight or a gladiator and assume that persona out in a vacant field somewhere with other people who are doing the same thing.
Paul has none of those things in mind when he tells the Corinthians to man up. He is telling them as simply and straightforwardly as possible to be bold, sober-minded, mature, and committed to their calling—like soldiers. Be valiant soldiers in the battle for truth.
In fact, notice the two imperatives on either side of this command to act like men. They explain the true gist of it: "Be steadfast." "Be strong." Those are character qualities. And sandwiched between them is this: "Act like men." The imperatives in that string of commands basically explain one another. Strength, steadfastness, courage, and even vigilance—these are all vital aspects of what Paul means when he says, "Act like men."