To "provide (someone) with assistance" just means to help them. So the following phrases have nearly the same meaning:
Any assistance you can provide would be greatly appreciated.
Any help you can give would be greatly appreciated.
But "assistance" is a more formal word than "help".
"Provide" is also formal. It means to give something or to make something available for people to use:
These results provide support for the theory that humankind evolved speech later than scientists had previously thought.
"Provide ___" is really common in writing. Here are some of the most common things that people "provide":
provide health care