The phrase "out-of-pocket expenses" refers to a cost paid by an individual by, more or less, taking the money out of their own pocket. For example, imagine you take the company car across town on company business; on the way you realize the vehicle is almost out of gas and, having no other option, you fill up the tank and pay for the gas with your own money.
This is obviously a different situation than would obtain if you had paid for the gas with a company credit card. Most out-of-pocket expenses related to business are theoretically reimbursable by the business, but various policies will govern what expenses will be reimbursed. Some unreimbursed out-of-pocket expenses may be deductible from income tax.