There is a conversation in the film about Jenny's death, during which she tells Forrest that she is sick.
The script is excerpted as follows:
JENNY: Forrest, I'm sick.
FORREST: What, do you have a cough due to cold?
JENNY: I have some kind of virus. And the doctors don't, they don't know what it is. And there isn't anything they can do about it.
Considering the film's background and based on this conversation, we can guess that Jenny dies of complications from AIDS. The film does not explicitly reveal this, but it is implied that Jenny has this disease. This 'mysterious virus' was not officially named AIDS until the mid-1980s. Jenny died in 1982, so when she mentions her virus to Gump, AIDS had not yet been named.
In fact, in the first book, Jenny does not die, nor is she sick. Forrest is a professional wrestler, while he and Dan gamble on his wrestling matches to make money, and Jenny leaves Forrest.
Forrest eventually loses all his money, along with Jenny, as she marries someone else.
However, when filming, the director or the screenwriter adds a new plot element. They use Jenny as a way to criticize the new values of the society of the 1960s and '70s. Jenny, as a part of the 'lost generation', is pure in nature, but experiences social changes such as sexual openness, the Vietnam War and the spread of recreational drugs. Her society leaves her with nothing but AIDS.
Forrest is a popular character due to his love of running, while also symbolizing young people's stubbornness and reflecting a sense of resistance that is different from others of his era.