In one sentence
Dharma is the right way of being and acting in a given context — what is owed by you, from where you stand, in the situation you are actually in.
The depth — what it actually means
Dharma is one of the hardest words in Sanskrit to translate because English wants one of two things: "duty" (which sounds rigid) or "law" (which sounds external). Dharma is neither. It is the right action in this particular situation, performed by this particular person, with this particular history, in relation to these particular others. It is contextual without being arbitrary. The Gita constantly returns to dharma because Arjuna's entire crisis is a dharma conflict — duty to family vs duty to caste vs duty to truth. The book does not give him a universal answer. It gives him the tools to find the answer that is his.
Modern application — how to use this today
In your own life: when faced with a moral choice, do not ask "what is universally right?" Ask "what is right from where I actually stand, with the responsibilities I have actually taken on, given who I actually am?" The answer to the first question is philosophy. The answer to the second is dharma.