According to Osho, they are called purusharthas because each aim reveals the artha—the inner meaning—of the person. What you chase declares who you are: pursuing wealth shows clinging to the petty; kama exposes bondage to desire; dharma reflects a heart seeking truth; and longing for moksha discloses the soul’s thirst for ultimate freedom.
They’re called life-aims because whatever you run after—money, pleasure, goodness, or freedom—shows who you really are inside.