"Grants management" relates to all of the administrative tasks required to handle the money, reporting, and program implementation in a way that meets generally accepted standards as well as the requirements of the funding source.
You don't necessarily need a software program. The funder wants to know that the accounting and financial systems are in order and can adequately keep track of and report on income and expenditures--it’s great if you’re able to state that your books are audited annually by an independent CPA. The funder wants to know that your organization can handle the required reporting (both fiscal and programmatic) and has a track record of meeting deadlines.
You also need to address how your organization will oversee program implementation. Is strong leadership in place that will ensure the program operates as planned, document progress, and manage it appropriately? Application guidelines usually lay out the information the funder wants to see.
By the way, what one funder calls "grants management" another may call a "management plan." Some funders may expect to see this sort of information presented in the section on “applicant background” or “applicant experience.” Check out The Grantsmanship Center's publications on grant management written by Henry Flood. They're on the Publications for Purchase section of this website, under the RESOURCES section.