They are quite bright students (they even have their own twin language commonly known as Cryptophasia) and are often very conniving and mean, even to each other. When it comes to Bart they are quite stuck up, and never miss an opportunity to berate him. Bart appears to have a crush on one of them, but Homer states that Terri is the one that Bart has a crush on. One of the twins stated that her sister had a crush on Bart. It is unknown if this is the truth or if it is just teasing. She also has a "boy crazy" cousin who has a crush on Bart. (Bart feels affection for her and she may also feel affection for him).
When it comes to Lisa Simpson they are just as inconsistent. One minute they will be friends on the schoolyard playing together and the next they will be ganging up on her. More often than not it is the latter, usually not including Lisa because she is too smart or too weird. It is implied that she and Sherri are actually two out of three triplets who were conjoined and it is said the third triplet is trying to kill them, but that can be viewed merely as a throw-away joke by the writers, and should not be regarded as canon.
Principal Skinner apparently considers Terri less smart or talented than Sherri, because in Simpson Tide he announces, "In the event of nuclear war, we can only save our best, and brightest. Therefore, space in the fallout shelter will be reserved for: Lisa Simpson, Martin Prince, our championship kickball team, and Sherri, but not Terri." Both the twins Sherri and Terri have creamish-like pale-yellow skin and dark bright purple hair.
The contents of this article or section are considered to be non-canon and therefore may not have actually happened/existed.
In "Barthood", it is revealed that in the future, Bart enters a relationship with Terri. When he throws a party, he accidentally makes out with Sherri who remarked he kisses just like Terri said. He is shocked and asks, "Wait, you're not Terri?" and awkwardly backs away when Sherri tries to continue the encounter. It is unknown what became of this relationship. 
Nelson Muntz simultaneously dated and impregnated both Terri and her sister, who bore him four children (two sets of twins, naturally) shortly before Nelson's high school graduation. It's implied that one of the twins tricked him into thinking he was with the other. He abandoned them during Bart's graduation party, using the same statement his father said to him before abandoning him.
The Simpsons Arcade game
Sherri and Terri appear in stage 1 and 2 carrying a burger in a plate for the Simpsons to gain their health.
The Simpsons Game
Sherri and Terri were one of the holders of the three Sparklemon that Homer and Lisa must defeat.
Behind the Laughter
They have similarities to the Grady Twins (ghost girls) Danny sees in Stanley Kubrick's adaptation The Shining, of Stephen King's The Shining novel of the same name. In a deleted scene of the parody of the Shining called "Treehouse of Horror V" they are ghost twins seen by Bart. They also take on this role in The Simpsons Game were in a game engine elevator they are heard saying "Come Play With Us Simpsons". She is said to be the taller of the two.
Terri is the one on the right as it was stated by Matt Groening that Sherri is always on the left.
Both she and Sherri bear some resemblance to the twins Patty and Selma, as both hold an enjoyment for tormenting the males of the Simpson family, but for different reasons, and have a close relative who have a crush on one of the Simpsons.
It is implied that Sherri and Terri aren't actually twins, but 2/3rds of conjoined triplets. This has to be considered just a throwaway joke by the writers, as this 'third triplet' has never been shown or mentioned before.