Oskar's father meets his mother while he's recovering soldier in a hospital where his mother's a nurse. He's an ethnic German. Even though she's in love with someone else, he wins her heart with his cheerful manner and soulful cooking. After the war (WWI), he stays on in Danzig and becomes a salesman for a paper company. (Dunder Mifflin?) After marrying Oskar's mother, he buys a struggling grocery store in the suburbs. When his son (is it really his son?) Oskar's born, Alfred's first thought is:
He'll take over the business someday. At least now we know why we've been working our fingers to the bone. (3.33)
But for all of his ambitions to leave behind a legacy, Alfred fails. His son refuses to grow up at all. As Oskar puts it at one point, "Matzerath simply lacked judgment" (21.9), even though "he always thought highly of himself" (21.19). This might help explain why Alfred manages to remain so oblivious for so long about the fact that his wife is having an affair.
An example of his colossal lack of judgment is his decision to serve eels for dinner after his wife is still traumatized by the experience of seeing the disgusting way in which they were caught. His insistence on her eating the eels triggers Agnes's compulsive fish-eating that eventually kills her.
From day one, Alfred seems destined for disaster. He's a practical guy, but not really intelligent or competent enough to capitalize on his opportunities. He needs his wife Agnes to keep the books for his store and to make it more efficient. And after she dies, he needs the young Maria Truczinski to take her place and do the same thing. Even after Maria pulls his shop back to respectability, though, Alfred takes the credit:
"After all, I'm the one who hired the girl and taught her the business." (21.20)
Alfred constantly lives with the guilt of leaving the basement door open and allowing Oskar to fall down the stairs. This might be the reason why he won't let the government institutionalize him.
"It's out of the question, I promised my wife on her deathbed." (28.6)
The one thing that Oskar seems to truly respect about his "presumptive" father Alfred is the man's ability to cook. Oskar claims that many of the best meals of his entire life were cooked by Matzerath, and that the man was a cooking genius.
Alfred becomes a member of the local Nazi party organization. As a German, he welcomes Danzig being unified with Germany, but it's unclear how much he buys into the ideology.
[…] Matzerath, who recognized the forces of law and order early on and joined the party in thirty-four, yet even so never advanced beyond cell leader. (9.30)
Seems like he just saw which direction the wind was blowing and wanted to be on the winning side. But his party affiliation ends up getting him killed. When the Russian Army invades Danzig, Alfred's hiding with the family in the cellar. He tries to ditch his Nazi insignia pin, and eventually tries to swallow it. His choking provokes the Russian soldiers, and one of them shoots Alfred to pieces. Oskar also feels responsible for killing Alfred by handing him the pin.