What difference would filing as a widow make as opposed to filing single?

[IreneS]

Qualifying Widow (or widower) is a filing status for someone who lost a spouse in the two years prior to the current tax year (2014 or 2015), did not remarry by the end of 2016 and has a dependent child you lived with you all of 2016.  You must also have paid over half the cost of keeping up the home.

This is a favorable tax provision because it allows the QW to essentially use the same tax rates as if they were married filing jointly.  If they don't qualify as a QW, they'd have to use the less favorable single or head of household rates.