As, we know the term "Stithpragya" is mentioned in Bhagavad Gita.But what is actually meaning of the Stithpragya.?
Para sympathetic state of mind is known as Stithpragya. We all live in the sympathetic states with period of anxiety and depression always . In Bhagwat Gita Krishna described the stithpragya , state of mind as the state where both loss and gains does not affect an individual.
We are happy to see things through; when the going is good. But in trying times, our happiness just disappears. It is here that a balance is required to be maintained. In the Holy Gita, Lord Krishna taught Arjuna the process of maintaining equilibrium (Stith Pragya) in all situations. Lord Krishna exhorted Arjuna to repose his entire faith in Him. Krishna wanted Arjuna to play his role without worrying for the result of his actions. So, it is best to adjust with the circumstances when they do not seem favorable and wait for good times.
Now let's understand from the Bhagavad Gita Chapter 2
arjuna uvāca sthita-prajñāsya kā bhāṣā samādhisthasya keśava | sthita-dhīḥ kiṁ prabhāṣata kim āsīta vrajeta kim || 2.54 ||
Arjuna said: What is the mode of speech, O Krishna, of one of steady wisdom who is established in the control of the mind? What will one of steady wisdom say? How does he sit? How does he move?
śrī bhagavān uvāca prajahāti yadā kāmān sarvān pārtha manogatān | ātmany-evātmanā tuṣṭaḥ sthita-prajñās tad-ocyate || 2.55 ||
The Lord said: When one relinquishes all the desires arising in the mind, O Arjuna, when one is satisfied in oneself with the Self, then one is said to be of steady wisdom (sthita-prajña).
This is the highest form of devotion to enlightenment. Then, the lower state, not far below it, of one established in steady intellect, is described;—
duḥkheṣv-anudvigna-manāḥ sukheṣu vigata spṛhaḥ | vīta-rāga bhaya krodhaḥ sthita-dhīr munir ucyate || 2.56 ||
One whose mind is not perturbed by pain, who does not hanker after pleasures, who is free from desire, fear and anger — is called a sage of steady intellect (sthita-dhi)
Even when there are reasons for grief like separation from beloved ones, the enlightened one’s mind is not perturbed. He has no craving for sense enjoyment, he has no hankering for them. He is free from desire, fear and anger;— desire is craving for objects not yet obtained. Fear is mental agitation produced by the awareness of factors which cause separation from objects that one loves, or by encountering that which is undesirable. Anger is a disturbed state of mind which produces aggression directed at another sentient being who is perceived as the cause of separation from the beloved object or when confronting what is undesirable. An aspirant of this sort, who constantly meditates on the Self, is said to have attained steady intellect.
yaḥ sarvatrān-abhisnehas tat tat prāpya śubhāśubham | nābhinandati na dveṣṭi tasya prajñā pratiṣṭhitā || 2.57 ||
He who has no attachment anywhere, who, when encountering the agreeable or the disagreeable feels neither attraction nor aversion — his wisdom is firmly established (prajñā-pratiṣṭhitā).
One who has no attraction at all for pleasing objects, ie., who is indifferent to them, and who does not feel either attraction nor repulsion when involved with, or separated from attractive or repulsive objects respectively, who neither delights in the former, nor is repulsed by the latter — has attained established wisdom.
yadā saṁharate cāyaṁ kūrmo’ṅgānīva sarvaśaḥ | indriyāṇīndriyārthebhyas tasya prajñā pratiṣṭhitā || 2.58 ||
When one is able to withdraw the senses from the objects of senses on every side, as a tortoise withdraws its limbs, then one's wisdom is firmly established.
When one is able to draw the sense-organs away from the sense-objects like a tortoise withdrawing all its limbs, and fixing its mind on its Self — he too is said to have attained steady wisdom. Thus there are four stages in the progression to enlightenment38, each stage giving rise to the succeeding stage. Now Sri Krishna speaks of the difficulties of [both] the attainment of resolute dedication to enlightenment and the means of that attainment.
It is very important to maintain the steady wisdom,on the path of self-realization, but it is also very diffcult to maintain steady wisdom that is also declared by lord himself you can look out the Chapter 2 Sloka 59 onwards.
But to reach Supreme Abode we have to be Steady and purely devoted to Supreme Lord Krishna (Narayan)