A voucher check is a standard 8.5 x 3.5 inch business check with one or two attached stubs — the "vouchers" — that record details about the payment: date, payee, amount, and often an invoice number or memo.
What the stub is for
One stub is usually kept by the business for its own records, and the other (if there are two) can be detached and given to the payee as a payment receipt. This is especially useful for payroll, where the stub becomes the employee's pay statement.
If you're choosing check stock for a business, voucher checks are the standard default — they're what most pre-printed business checks look like, and what accounting and check-printing software typically assumes by default.