It is a formulaic expression used at the end of formal letters (in which the writer apologizes for something), and means something like:
"Please excuse our informality, but we hope you will accept our (quickly) written expression of apologies."
This sounds like a mouthful in English because we usually do not write as much in our formal correspondences, and would probably opt for something like "Please accept our most sincere apologies in miscalculating the total sum for your order in our previous invoice."
This letter basically explains why there was a mistake in the order total, and that the company has addressed the problem, and that a new corrected invoice is included in the same letter. The company asks the customer to discard the old invoice.