Embarrassingly tells you that something happens in a way that makes you — or someone else — feel ashamed, nervous, or uncomfortable, or that it is true to a degree that makes people wince. You might say you embarrassingly forgot a name. You might say a film is embarrassingly bad, meaning it is so bad you feel awkward watching it. It is an adverb: it tells you how, or how much. It does not name the thing itself. People use it in talk and in writing when they want to admit a small social fail, or to judge something as awkwardly too much. The feeling is social: you are not in danger, but you wish the moment would end.