In plain words
Whenever dharma declines and adharma rises, Bharata, then I manifest Myself.
Word for word
Whenever, indeed, there is a decline of dharma, O Bhārata, [and] a rise of adharma, then I send forth Myself.
The commentators
Bhagavadgītābhāṣyam
तच्च जन्म कदा किमर्थं च इत्युच्यते —
यदा यदा हि धर्मस्य ग्लानिः हानिः वर्णाश्रमादिलक्षणस्य प्राणिनामभ्युदयनिःश्रेयससाधनस्य भवति भारत, अभ्युत्थानम् उद्भवः अधर्मस्य, तदा तदा आत्मानं सृजामि अहं मायया ॥ ७ ॥
In plain words
And that birth: when does it happen, and for what purpose? To this the answer is now given:
Whenever dharma weakens — dharma meaning the whole ordering of varṇa and āśrama and all that goes with it, the very thing by which living beings both flourish here and reach the highest good — and whenever adharma stands up openly, then, Bhārata, every single time, I bring myself into form through māyā.
Close to the Sanskrit
And that birth — when, and for what purpose? — thus it is said:
Whenever indeed there is glāni — decline — of dharma, of that dharma whose mark is varṇa, āśrama and the rest, which is the means to the prosperity and the highest good of living beings, O Bhārata, and abhyutthāna — the rising up — of adharma, then and then again I send forth my own self by māyā.
Gītā Vāhini
భగవంతుడు చెప్పిన చొప్పున “ధర్మమునకు హాని సంభవించినపుడంతయూ నిరాకారుడైన నేనే నరాకారమున అవతరించి ధర్మమును ఉద్ధరింతును. సాధులను కాపాడుదును” అన్న విషయమున కొంత సంశయమునకు స్థానమేర్పడినది. సామాన్య మానవులకు ధర్మము నశించునట్టిదనియు, నిత్యమైనది, సత్యమైనది కాదనియు తలంచుటకు అవకాశమున్నది కదా?
In plain words
God has said, “Whenever harm comes to Dharma, I Myself, the Formless One, descend in human form and raise Dharma up. I protect the good.” About this statement some room for doubt has arisen. Ordinary people have occasion to think, do they not, that Dharma is something that perishes, that it is neither eternal nor Satya?