Speedy spends most of this story drunk. Well, not drunk, but in something of a haze that's totally not his fault. So we don't get to know much about Speedy in this story except that a) he's expensive and his self-preservation instincts have been strengthened and b) he knows a lot of Gilbert and Sullivan operas.
Speedy demonstrates how the Three Laws of Robotics interact; in this case, the Laws get in each other's way. Because Speedy cares about his own self a lot (Third Law), he can't quite obey a weak order (Second Law), which locks him up in this dilemma, which causes him to act drunk and sing Gilbert and Sullivan show tunes.
But when Speedy does snap out of it (thanks to the First Law), we see another robot that seems human. For instance, here's Speedy's first line of dialogue—which is the first line we hear from any robot:
Holy smokes, boss; what are you doing here? And what am I doing—I'm so confused— (229)
Does that sound like a typical "beep-boop-beep" robot to you? No, once again, Asimov reminds us how human his robots can be.
What does this robot tell us about robots? Still very human, Speedy demonstrates how the Three Laws of Robotics interact with each other and can sometimes tangle each other up. But still, the First Law is above all other laws.