In the Simpsons episode "Lisa the Simpson", it is established that Homer and Bart carry the Simpson gene, which contributes to baldness and laziness.
Good thing Lisa isn't going to be affected...
Effects on different genders
Doctor Simpson explains that the Simpson gene is on the Y chromosome, and so only affects males, (although Homer's half-sister Abbie is clearly affected by the gene) meaning that Lisa and Maggie are unaffected. This was proven further in the comic, when several of them during a reunion where sharing stories about their successful lives.
Despite her above average intelligence, Lisa has, on occasion, shown some of Homer's traits such as saying "D'oh!" when she encounters trouble or misfortune, indicating that she IS influenced by the Simpsons gene, but only to a small extent.. However, many people not in the Simpson family have used that exclamation in the past. Lisa has also inherited Homer’s chubby fingers.
Degree of Effect on Male Simpsons
While the Simpson gene does affect every Male Simpson, it does not always affect them to the same degree. Homer's half-brother Herb was able to graduate from Harvard and start up his own successful company. He was still affected by the gene however in small bursts of idiocy and recklessness (e.g. letting Homer design a car and spitting out of a hot air balloon into the street).
Though Bart has a mischievous personality, the gene hasn't actually had an impact on his intelligence, as he plans his pranks before committing them, and was able to discover that Sideshow Bob framed Krusty and was planning to kill Selma for money. Homer and Bart have also displayed high levels of intelligence and ability in specified areas (e.g. foreign language and music) both display an incredible sense of accuracy. Bart with firearms and Homer with bowling (eventually scoring a perfect game) which they could be seen as Savant Syndrome for. In "Bart's Comet", when everybody was panicking over the comet, Homer theorized that Springfield's polluted atmosphere would prove beneficial as it would burn up the comet and sap its destructive power. After Lisa remarked that Homer was indeed correct, he claimed he was scared by his own accuracy.
Homer Simpson Syndrome
Homer has an unusual condition — "Homer Simpson Syndrome" — where his brain is cushioned by an especially thick layer of fluid, acting as a helmet of sorts. It is unknown whether the Simpson Gene causes Homer Simpson Syndrome, though the males in the Simpson family seem to have a thing for putting pots and pans on their heads and head-butting, suggesting a connection.
Other reasons for Homer's stupidity
in the episode "HOMЯ", Another reason for Homer's stupidity is that a crayon was lodged into his brain when he was six. His IQ without the crayon was 105, placing him in the "average" bracket (90 to about 110, generally). However, in that episode, he was regarded as a "genius."
Homer's obsessive binge drinking may also be a factor. As Homer says in "Treehouse of Horror IV", "Oh, Lisa. You and your stories. Bart is a vampire, beer kills brain cells. Now lets go back to that... building... thingy, where our beds and TV... is." However that was a Treehouse of Horror episode and therefore non-canon.
In "Itchy & Scratchy: The Movie", he tells Bart about how he wanted a bike when he was a kid, but his dad wouldn't let him. So he holds his breath until he passed out. He mentions that the doctors told him he had brain damage.
In "Marge on the Lam", he once went to a military camp for experimental testing to get out of Patty and Selma's visit. The doctors warned him that his injections would result in hair loss and lower intelligence. Homer says it was worth it.
He may have also become intellectually challenged due to low self-esteem from Abraham Simpson always putting him down. This is reinforced by Homer's statement in the episode "Grampa vs. Sexual Inadequacy" that if only Abe hadn't put him down, he might have more of a chance at being successful.
Biological interpretation of the episode
Homer has the defective Simpson gene located on the Y-chromosome. The Simpson 'gene' is actually an allelic anomaly that exerts phenotypic dominance over its counterpart locus on the X-chromosome donated by his mother, regardless of the fact that they are non-homologous. Because it is a dominant allele in this hemizygous condition, the exceptional intelligence that would result from the expression of the allele on the X chromosome is repressed. This repression allows for the expression of only the Simpson 'gene' and causes mental inertia to begin at approximately age 8 and continue to increase in severity until adulthood when it plateaus. Homer's intelligence is therefore naturally below average due to his genetic condition, but his years of work at the nuclear plant have mutated his Y-chromosome and have rendered his Simpson allele inactive. This grants him not only normal intelligence but exceptional intelligence (facilitated by the unblocked allele locus on his X-chromosome inherited from his mother). This intelligence, however, is not expressed because of a crayon lodged in the frontal lobe of his forebrain (a key area of regulation for cognition and behavior) since he was a child (But he could not have been too smart when he was child to put crayons up his nose). It had been removed, revealing his extraordinary intelligence but he insisted it be re-lodged to restore him to normal social status of moron, rather than "nerdy genius".