First, the mix-up everyone makes: Oppenheimer & Co. is a New York investment bank and wealth manager. It's not OppenheimerFunds, the fund company now part of Invesco. Make sure you're applying to the right one, and don't confuse them in an interview.
What it does
Oppenheimer has a mid-sized investment bank working on capital raising and M&A, with groups in areas like healthcare and technology, alongside a big wealth management business.
Applying
Mainly a US application. For US students it's a reasonable middle-market option, often with smaller classes and less competition than the big names.
On the resume: the usual. Deal or modelling work with numbers, a leadership role with a result, GPA if strong, and an early application.