Mr. Fitzgibbons owns and works the farm which hosts a plethora of wild animals during all seasons of the year.  His main field, which is alternatively called the "garden" by many of the wild animals, provides a comfortable home for them during the winter months, when the field isn't being plowed, planted, or harvested.  When it is, especially at the start of plowing time--which the animals refer to as "moving day"--they all clear out for their summer homes off of the farm property...usually into the fields and the forest beyond.  Farmer Fitzgibbons owns a large tractor, with a multi-bladed plow, which churns up the field and the animals' winter homes in the process...everywhere, except for the dirt immediately around the leeward side of a large stone jutting from the ground at the far end of the field, where the Brisby home is located.  Unfortunately, it's located on the windward side, vulnerable to the plow.  And it will take the help of the rats to move it to the protected side.

Meanwhile, Farmer Fitzgibbons is mildly irked by what appears to be a recent rat infestation in the ground under his wife's rose bush, which he would like to see eliminated!

Quote: "Morning?  Suits me fine.  No no!  No, you can bulldoze that rose bush right out of there.  I want those rats exterminated!  Now, uh...there's no charge, right?"

Origins of the character: In Robert C. O'Brien's book "Mrs. Frisby And The Rats Of NIMH", the family's name is "Fitzgibbon" (without an "s" on the end, as in the movie).  We never learn Farmer Fitzgibbon's first name.  And there isn't much of a description of him.  However, the book presents him as an honest, hardworking farmer and family man, earning his daily keep.  He has two sons, Paul (who does not appear in the movie) and Billy.  His wife is also present in the book, though she's only ever referred to as "Mrs. Fitzgibbon".

In the animated sequel: Though we do see the Fitzgibbons farm in the sequel, none of the Fitzgibbons family itself are ever seen during it.