Moon/Mars combines the Moon's association with emotions, emotional care, and emotional bonding with Mars' association with action, bravery, assertiveness and argumentativeness:
The Moon/Mars combination in the chart of yoga master B.K.S. Iyengar can be seen in the style in which he cares for and nurtures (Moon) his students by encouraging them to be very active (Mars): https://www.youtube.com/watch?v=SgEC9uxFDQo
In your astrological birth chart the Moon symbolizes your emotional identity. It reveals where we are emotionally comfortable and says a lot about the ways in which we emotionally bond with others. As a signifier of comfort and emotional bonding the Moon also symbolizes women, children and the home.
In your astrological birth chart, Mars is represented by a circle with a spear-like arrow pointing out. This is the same international symbol used to represent men (whereas the symbol for Venus is used to represent women). Just like it’s spear-like shape hints, Mars is associated with sharp action, argumentativeness, bravery, and assertiveness. Mars wants to heat things up and create athleticism and competition.
When you find the two aligned in a birth chart the soft emotionally bonding nature of the Moon gets prodded by Mars’ spear-like aggressiveness. In turn Mars tends to heat up and invigorate the Lunar association with comfort.
What do you get when you see when you put the two together?
The Moon/Mars combination is great for people that prod us out of our comfort zones. Film maker Michael Moore is an excellent example of this. His politically charged movies aim to prod (Mars) the viewers out of their complacency in their comfort zone (Moon).
Actor Sacha Baron Cohen provides another fine example of this. In a humorous way he tricks the people he interviews into revealing their true views and motives. In order to accomplish this he often throws himself headlong into roles that antagonize (Mars) the comfort level (Moon) of the audience. Perhaps the symbolically appropriate example of this can be seen in his fake congressional proposal to arm (Mars) children (Moon) with guns: https://www.youtube.com/watch?v=QkXeMoBPSDk
Malala Yousafzai provides an activist example in that she fought against (Mars) the cultural norms and comfort levels (Moon) in her native Afghanistan by becoming an activist (Mars) woman (Moon) on behalf of education for women in her country.
Marie Kondo provides another great example. She is an expert at organizing homes. As a television personality she enters homes and helps the homeowners to activate and invigorate (Mars) their home-life (Moon) by clearing their home of clutter.