First a few terms:
Low Earth Orbit (LEO) All spacecraft must first achieve low Earth orbit. This is true whether you're sending stuff to the Moon or Mars.
Trans Mars Insertion (TMI) The burn needed to send something on its way to Mars.
Delta-v Change in velocity needed. Usually measured in kilometers/second. An important metric for space missions.
Earth Moon Lagrange 1 (EML1) A region between the Earth and the Moon where the Moon's gravity and centrifugal force balance the Earth's gravity.
Earth Moon Lagrange 2 (EML2) A region beyond the far side of the Moon where centrifugal force balances the Earth's and the Moon's gravity.
Delta-v to get from LEO to the Moon's surface is about 6 km/s. To get out of the Moon's gravity well is around 2.5 km/s.
From LEO, TMI is about 3.6 km/s. From LEO it take less delta-v to send something on its way to Mars than it does to send a payload to EML1.
So, if all propellent and materials come from the Earth, we gain nothing from launching from the Moon's surface. It is better to launch from LEO.
However, there may be water ice deposits at the lunar poles. If so, it might make interplanetary flight easier, if we exported lunar propellent and life support consumables to EML1 or EML2. A Mars-bound vehicle could stop at EML1 or EML2 and stock up on propellent, water, and air before departing from Mars.
As the delta-v map indicates, the Lagrange regions are close to other destinations of interest besides Mars.
However, it remains an open question, if there are rich volatile deposits in the lunar cold traps.