Embarrassed means red-faced because something awkward happened in front of other people. The wish that the floor would open.
The audience is the essential part, since almost nothing is embarrassing when you are alone. It takes about or by, and it differs from ashamed in the cause, because shame follows a wrong and embarrassment follows an awkwardness. English also has financially embarrassed, a polite old phrase for having no money. Watch the spelling, with two r's and two s's, which is one of the most commonly misspelled words in the language.
1adjectiveembarrassedFeeling awkward and self-conscious in front of others.
“He was embarrassed about forgetting her name.”
Past participle of embarrass.
Etymology from Wiktionary, CC BY-SA