Not ashamed and not embarrassed — especially when most people in that situation would be. The word only makes sense against an expectation: someone has done something unusual, cheeky, sentimental, or rude, and instead of shrinking, they carry on openly. "He was unabashed by the laughter" means the laughter did not touch him. It often describes a manner rather than a moment: unabashed delight, unabashed curiosity, an unabashed romantic. Interestingly, the feeling attached to it is often admiring rather than critical — being unabashed about loving a silly song or crying at a film sounds honest and free, not shameless. But it can tilt the other way too, when the thing not being ashamed of is something the speaker thinks should embarrass a person. Which way it leans comes entirely from what follows it. There is also the adverb unabashedly, which is common. The word is a bit literary — you will meet it far more in writing than in casual speech.