Four words that carry everything
Dharma is right living, karma is action and its consequence, samsara is the cycle of rebirth, and moksha is freedom from it.
Dharma is what upholds. It is your duty, the right way to act from where you stand in life, and the order that keeps the world from falling apart. It is not one rule for everyone: a student's dharma is not a parent's, and neither is a ruler's.
Karma means action, and the principle that every action shapes what follows. It is not fate and not punishment; it is cause and effect applied to a life. The Bhagavad Gita's most quoted verse is about it: you have a right to your work, never to its fruits (2.47).
Samsara is the cycle of birth, death, and rebirth. The Gita compares it to changing worn-out clothes (2.22). What you do now is what you carry forward.
Moksha is liberation — release from that cycle and from the confusion that keeps it turning. Schools describe it differently: union with God, realising the self as Brahman, or eternal loving service. Most Hindus treat it as the far horizon. Dharma is the road today.
Tradition names four aims of a human life: dharma, artha (means and prosperity), kama (enjoyment), and moksha. The first three are lived inside the frame of the fourth.
In the tradition's words
कर्मण्येवाधिकारस्ते मा फलेषु कदाचन । मा कर्मफलहेतुर्भूर्मा ते सङ्गोऽस्त्वकर्मणि ॥
Karmaṇy evādhikāras te mā phaleṣu kadācana, mā karma-phala-hetur bhūr mā te saṅgo'stv akarmaṇi
Your right is to the action alone, never to its fruits — and that is no excuse to do nothing.
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Where this comes from
Bhagavad Gita 2.47 and 2.22. Brihadaranyaka Upanishad 4.4.5 ("as one acts, so one becomes"). The four aims (purusharthas) are set out across the Dharmashastra literature.