There was a huge twist waiting: the 'Jessica' who first joined the team turned out to be the shape-shifting Skrull queen Veranke in disguise. When the real Jessica was rescued during Secret Invasion, she and Peter had to rebuild their trust from scratch, and their friendship came out stronger for it.
As a trained spy, Jessica brings skills Peter doesn't have. She goes undercover, gathers intelligence, and thinks three steps ahead, while Spider-Man brings the jokes and the raw acrobatics. Together they cover each other's blind spots, which is exactly why they were both picked as founding members of the relaunched Avengers.
In the classic comics Jessica Drew and Peter Parker mostly kept to separate corners of the Marvel world. Their real relationship began in the 2000s when both joined the New Avengers and fought side by side. There was a catch worthy of a spy story: the Jessica who first sat at the table was actually the shape-shifting Skrull queen Veranke. It was only after Secret Invasion, when the true Jessica Drew was rescued from Skrull captivity, that she and Peter built the honest, tested friendship they share today.
Jessica has continued to headline her own series (most recently the 2020 run by Karla Pacheco), working as a bodyguard and private investigator while raising her son, Gerry. She remains part of the wider Spider-family and drops back into big multiversal events, where her bond with Spider-Man is that of old teammates who trust each other completely.
Jessica Drew gained her powers as a child on Wundagore Mountain, where her scientist father's experiments with spider-based serum saved her life but left her changed. Raised and trained in secret by the terrorist group HYDRA, who told her she was working for the good guys, she eventually learned the truth and turned against them to become a hero.
As Spider-Woman she can stick to walls, has superhuman strength and speed, and fires crackling bio-electric 'venom blasts' from her hands. She can also glide on webbed underarm gliders and gives off pheromones that affect the people around her. On top of all that she is one of Marvel's sharpest spies and investigators.