Team Rocket is a organisation dedicated to using Pokemon for crime. This involves stealing Pokemon, getting money by offering Pokemon as gambling prizes, using Pokemon to steal, etc.
Two well known members of Team Rocket are Jessie and James. Those two are not very good at being Pokemon thieves but they are good with Pokemon, even if they don't win a lot of battles.
Jessie and James have a talking Pokemon, a Meowth. It doesn't technically belong to them; they are not its trainers, but they're a team, partners.
Jessie has an Ekans that she got for her birthday, while James fights with a Koffing he got for Christmas. Both trainers seem to favour poison Pokemon.
In the episode 'Dig Those Diglett', Ekans and Koffing evolve into Arbok and Weezing.
Jessie and James aren't out to get Pokemon for themselves; they're trying to capture rare Pokemon for their boss so he'll be pleased with them. They don't do very well, however. But Jessie manages to, with a bit of 'help' from Arbok, capture a Lickitung for herself, while James gets a Weepinbell which evolves a few episodes later.
For some reason, Jessie keeps the Lickitung. I would've thought such a rare Pokemon would've made the boss happy, but hey, what do I know.
Main Pokemon used by members of Team Rocket are Meowth, Arbok, Weezing, Raticate (by Cassidy) and Persian (the boss). Most of these choices of Pokemon are pretty easy to understand.
It makes sense that Meowth should be the main TR Pokemon. Not only is it fairly cute/appealing to an audience, but more importantly, it represents money and greed with the charm on its forehead and its Pay Day attack.
In addition, cats are natural enemies of mice, and Pikachu is a mouse Pokemon.
Persian was probably chosen for similar reasons, and in addition its Pokedex entry attributes 'fickle meanness' to it. Perfect for villians.
Weezing and Raticate... I'm not so sure about them. Weezing is gas; poison, toxic. That sounds fairly evil. It's pure poison, pretty much. Raticate's just psycho looking. ^_^.
And Arbok. Good old Arbok. Snakes are naturally associated with evil, so it made perfect sense. However, having said that, the show didn't seem to take pains to make Ekans/Arbok seem terribly sinister or dangerous. (Although Arbok does sometimes look scary when it appears. ^_^.)
Arbok's role in Team Rocket is minimal. Team Rocket often perform their plans without assistance from their Pokemon. But while Weezing's gas is often used as a cover to hide them, Arbok is different. It's usually called upon to beat Ash so that they can finish whatever goal they were planning.
It may seem only a tool to help them steal Pokemon, but Jessie does care for her Ekans/Arbok, even if she doesn't have much faith in its abilities. As such, Arbok will probably never be able to reach its full potential, as Pokemon never can if their masters don't believe in them and help them to grow.