Vryjdfkk

I have started reading Bhagvat Gita.

I am going through Chapter-2 in which Shri Krishna explains Sankhya Yoga to Arjuna.

I would like to understand exactly what the Sankhya Yoga means ?

What is Sankhya Yoga ?

Why the lord tries to make Arjuna understand Sankhya Yoga ?

What is its importance ?

What does it means ?

According to Sridhara Swami, the meaning of the SAnkhya-Yoga of Bhagavat-Gita is as follows (Ref: Commentary of Gita, 2/39).

सम्यक् ख्यायते प्रकाश्यते वस्तुतत्त्वमनयेति संख्या सम्यग्ज्ञानं तस्मिन्प्रकाशमानमात्मतत्त्वं सांख्यं
samyak khyApate prakAshyate vastutattvam anayA iti samkhyA samyakjnAnam tasmin prakAshamAnam atmatattvam sAnkhyam.

Meaning:By which the Knowledge of the Self is properly revealed is called sankhyA.The yoga related to sankhyA is called SAnkhya-Yoga.

Acharya Sankar also reveals the same meaning :

[SAnkya means] the standpoint of Self-realization, with regard to the discriminating knowledge of the supreme Reality.

The same meaning has been derived by Acharya Ramanuja also:

Sankhya' means 'intellect,' and the truth about the Atman, which is determinable by the intellect, is 'Sankhyam.

Other commentators like Madhusudan Saraswati also connote the same implication :

सांख्ये सम्यक्ख्यायते सर्वोपाधिशून्यतया प्रतिपाद्यते परमात्मतत्त्वमनयेति संख्योपनिषत्तयैव तात्पर्यपरिसमाप्त्या प्रतिपाद्यते यः स सांख्यः। sAnkhye samyak khyAyate sarva-upAdhisunyatayA prtipadyte paramatmatattvam anayA iti sankhyopanishat tayA eva tatparyaparisamAptyA oratipAdyate.

So to conclude, the SAnkhya-Yoga of the Gita is the Yoga that reveals proper expression of the knowledge of the Supreme Self.

By the way, this SAnkhya-Yoga has nothing to do with the SAnkhya Philosophy propounded by Kapila Muni. Kapila Muni did not accept the concept of God as the existence of God can not be proved and so His philosophy is not being referred to in the Gita, which is based on the concept of God.