Wiktionary
vb. (context idiomatic English) To pretend to be all right or that everything is going well.
Usage examples of "keep up appearances".
Never again would he spend money he did not have just to keep up appearances, Adams vowed.
Of course I often have to perform bouts of snarling and jumping around just to keep up appearances.
He could keep moving, keep up appearances -- and keep himself alive.
Kynes's work with the Fremen threatened to put him in a conflict of interest as Imperial Planetologist, but he had to keep up appearances.
If you could imagine anyone obtaining this power of becoming invisible, and never doing any wrong or touching what was another's, he would be thought by the lookers-on to be a most wretched idiot, although they would praise him to one another's faces, and keep up appearances with one another from a fear that they too might suffer injustice.
This is the true Shakespearian wood -- but it is not the wood of Shakespeare's time, which did not know itself to be Shakespearian, and therefore felt no need to keep up appearances.
It was important to keep up appearances, even if everything else was falling apart around him.