If you bought a PS Vita before June 1, 2012 and live in the United States, you'll be eligible to receive the following:
$25 cash (in the form of a check)
$25 PlayStation Store credit
One of three game bundles ranging in value from $66.46 to $100.46 (see below)
According to the FTC's complaint, Sony claimed the Vita would "revolutionize gaming mobility" by allowing users to enjoy PlayStation 3 titles using Remote Play and take advantage of cross-platform play and cross-saves. But the FTC concluded that these assertions were misleading. See the full story here.
It's also important to note that, even though Sony has agreed to this settlement, the company "neither admits nor denies liability in connection with this matter." What's more, by accepting any of the offers, you are waiving your right to a future settlement. Full terms of the settlement offer are available here.
In addition to this PS Vita settlement case, Sony is now compensating PlayStation players for the infamous 2011 PlayStation Network hack. More details about that case and how to claim compensation are available here.