Use a single quote to escape the single quote.
$Application/Name='What''s new pussycat?'
Extra update (thanks to Tim van Steenbergen): use an extra single quote to escape.
In your screenshots, you put the full assignment instead of the value only.
Use an extra single quote before (thanks to Tim) the single quote in e.g. a Create Object (with entity Application) or Change Object (choose variable $Application) activity.
In the activity choose the Name attribute and set the following value:
'What''s New & FEEDBACK'