Mars is about action, engagement, moving forward, penetrating, conflict, independence and a few others. But what’s important to understand about mars in context to your question, is that it represents desire and destruction.
Mars is the part of human nature that WANTS to kill and destroy. It is quite literally the energy of destruction, death and aggression. Every human being has this in them, and many do not have outlets for it. And when it is not openly expressed it gets repressed OR it gets emotional. When it gets emotional it’s in a water sign, when it’s in Scorpio, it’s in it’s own sign.
Scorpio is the part of water that will kill you. When you see terrible waves, tsunamis, hurricanes, riptides etc, that’s Scorpio. Scorpio’s purpose on this planet, as an archetype, is to transform things. Death. When Mars is in Scorpio it speaks of a person, who wishes to transform others on the emotional plane. Generally, if Mars was doing it’s own thing in another element, it would probably just outright attack, or fight, or be aggressive towards whatever it wanted, with the intention of killing. (Note that this “killing” can be metaphorical and is not always literal). But in a water sign, it’s own sign, it is DEEPLY moved to find ways to get UNDER your skin. Because emotions are not a physical thing that we can see, Scorpios are considered hidden, generally speaking.
However, it also means that this person is easily threatened by emotional transformation, and possibly fears it. And can suggest that a person sees threats on the emotional front from others quite easily. And is willing to fight to ensure protection.
Very generally, a Mars in Scorpio person is a person who has a keen, if not unconscious understanding of what makes a person react, emotionally, and incites the things they wish to see in people. Any and all reactions will generally be hard to mask from such a person, because they are always looking out for it. This can be used to help people or not. It just depends on the person, and if it’s relevant to do so.
Scorpio in general, -needs- stability. But how it gains stability, is through validation of themselves by the reactions of others. And most people, who aren’t about getting their emotions all activated may find this intrusive, threatening, invasive, penetrating, scary, uncomfortable or generally unpleasant. This need for stability through constant emotional engagement is why it is a complementary opposite of Taurus, who is so earthy, that getting it to be roused would be hard, as emotionally, it really invests in it’s physical world, not the emotional one.
So, with Mars there, this person is much more invested or active in eliciting responses from people to see how they are and get some emotional truth from them. All in the name of their aggressive energy (Which is neutral) and to actively seek change (death) in themselves and other people.
So while jealousy and obsession are qualities of desire and desire is a quality of Mars they are only two qualities that represent a greater character that is Mars in Scorpio. So being in a relationship with such a person means you are signing up for wanting to die (figuratively speaking) because they desire intense emotional experiences and if you’re into that kind of thing well that’s a good place to be.