What is a waiver of notice, waiver of dependent administration and request for independent administration?

what is a waiver of notice, waiver of dependent administration and request for independent administration? My fiance's father passed away in November 2010. He didnt have a will but did have a lot of debt (IRS) as well as a lot of assets ( euipment, home, land, etc.....). My fiance's widowed step mom sent her this waiver of notice to sign in front of a notary and mail back to her. What is this and what does it mean? My fiance is an only child......please help!!!!!