What was Big Willy Shakes going for?
If the melancholy Jaques is a glass-half-empty kind of guy, then Duke Senior is the play's glass-half-full character. The first time we meet him in the Forest of Arden, he's living in exile because his little brother (Frederick) has stolen his dukedom.
Despite the fact that he's been betrayed by his own brother and now lives in a cave, Duke Senior doesn't let anything get him down. He tells us that, even though Arden is cold, windy, and rugged, it seems like the Garden of Eden to him. In Arden, he finds "books in the running brooks, sermons in the stones, and good in everything" (2.1.1). Wow, this guy is an optimist.
When Orlando bursts onto the scene, he says he and Adam "have looked on better days" (2.7.114). He asks if any of them can relate. If they can, then perhaps they can help him so his old friend doesn't die. At this point, it's pretty clear that Orlando is really desperate. He is being rude but he doesn't care because he's in such a pretty pickle.
Luckily, Duke Senior totally gets him. He knows what it's like to be in an unfavorable situation in life. He's in one himself. After all, his own brother stole his dukedom and forced him to live in the forest. He's "seen better days" to be sure. That's really just his nice way of putting that he's having a bad day now.
But Duke Senior is an optimist and he doesn't want to grumble. Instead he uses this nice little phrase to describe something not so nice.
The fact that both Orlando and Duke Senior know of this term tells us that most people in Shakespeare's audience probably would have understood this term instantly. It was used right around the same time in a play called Sir Thomas More. And Shakespeare used it again himself later in Timon of Athens.