Business casual means different things to different people. I usually interpret it to mean a dressing gown and slippers, but then I'm a bit eccentric.
Others will interpret it across a wide range of formality. It's easiest to describe these in terms of men's clothing -- adapt for a woman as appropriate:
- In Big 4 firms, quite a few people will wear a suit without a tie as business casual.
- In other firms, business casual is a pair of smart trowsers and a collared shirt.
- Particularly at American firms, business casual can mean chinos and a polo shirt.
As a rule of thumb, a man wants a shirt with a collar, trousers with a crease, and shoes that will hold a shine. That means no T-shirts, blue jeans, or trainers. Each firm is slightly different, but follow these guidelines and you shouldn't go far wrong.
Good luck and congratulations on your new job!