What is the reason behind the Lord Krishna stealing clothes of Gopikas and give them back after seeing their nudity ? What is the meaning of this story?
It was just a pastime of Lord Shri Krishna to test and teach the gopis a lesson. The gopis loved Shri Krishna very much and desiring to obtain Him as their husband they performed Kātyāyanī (one from of maa Durga) vrat for a month. On the final day of the vrat finishing their puja, the gopis went to Yamuna for bathing:
evaṃ purṇe ca māse ca samaptidivase tathā
snātuṃ prajagmugārpyaśca vastrāṇyādhyāya tattaṭe
Thus after the passing of one month, on the day of the completion, the gopis went to Yamuna for bathing carrying with them clothes, jewels, and many other things. [BVP - 4.27.8,9]
In a sportive mood they put their garments on the shore and went into the river without clothes. However, entering into water without clothes is offensive to varuna (the god of water). So to teach them a lesson, Shri Krishna and their friends took their clothes and hid at a distance:
vastrāṇādāya te sarve tasthurekatra dūrataḥ
śataśaḥ punjikāstatra sthāpayāmāsurunpukhā [BVP - 4.27.18]
Collecting the garments they went away and hid at a distance. Thus they gathered and created a heap of hundreds of clothes there.
Then Shri Krishna told the gopis:
saṃkalpite vratāha ca māse magalakarmaṇi
yūyaṃ nagnā: kathaṃ toye vratāṃgahanikārikāḥ
vrate tu nagnā yāsnātitāṃ ruṣṭovaruṇaḥsvayaṃ [BVP - 4.27.21,23]
You have vowed to observe the auspicious vrat for one month. Then how are you bathing in the water naked which is destroyer of the fruits of the vrat? Varuna (god of water )himself gets angry on him/her who baths naked in the water during the vrat.
When gopis found out that Shri Krishna and His friends had taken their clothes, they requested Shri Krishna to give them back:
O Śyāmasundara, we are Your maidservants and must do whatever You say. But give us back our clothing. You know what the religious principles are, and if You don’t give us our clothes we will have to tell the king. Please! [SB - 10.22.15]
Then, to test their surrenderness Shri Krishna spoke them as below:
The Supreme Personality of Godhead said: If you girls are actually My maidservants, and if you will really do what I say, then come here with your innocent smiles and let each girl pick out her clothes. If you don’t do what I say, I won’t give them back to you. And even if the king becomes angry, what can he do? [SB - 10.22.16]
After the gopis did as Shri Krishna told them, He returned their clothes. Thus after lovingly teasing and testing the gopis, the Lord granted their desire and told them that their wishes will be fulfilled:
Go now, girls, and return to Vraja. Your desire is fulfilled, for in My company you will enjoy the coming nights. After all, this was the purpose of your vow to worship goddess Kātyāyanī, O pure-hearted ones. [SB - 10.22.27]
The story is just symbolic. Krishna did not participate in human relations with the gopis (Radha-rani included). The gopis represent human beings - their clothes represent our attachments to this world (and our limited thinking). By taking away their clothes and asking them to come to him for it - he is is trying to teaches us to put away our worldly attachments and to go to him in a purified state. Once we surrender to him, the clothes will be given back because we will have understood their limited worth/significance. Radha-rani is the incarnation of the "Love of God" - that is why Krishna never married her - she was already "married", in a sense, to him from birth. That was why (even though she was born before Krishna) she only opened her eyes once she felt his presence - and looked at him (the Lord) before anyone else.
My answer is in sync with the accepted answer. I would like to add that Shri Krishna was a kid when he played all these Leelas. This is a point that is usually missed. Hence, to read more than what is there in it would not be a good idea:
If you read the Srimad Bhagvatam, you will find that he performed this Raas Leela (meaning: a pastime of the Lord) when he was just 14 years old. He was dear to everyone and would play with everyone. So do not emulate his ways but absorb all the knowledge that he has given through his life.
It is very difficult to be like Lord Krishna because he is Yogeshwar (Supreme among the Yogis). He could get away with hiding someone’s clothes while they were bathing! (Laughter).
If you carefully read about the leelas of Lord Krishna, you will not find that it is limited to one place or has only one kind of flavor. You will find every kind of flavor and color of emotion in the stories of Lord Krishna’s pastimes. There is humor, love, and even the pain of longing in his stories.
So he simply went through his pastimes to bring out each and every color and nectar of human emotion. It is impossible to completely understand the personality of Lord Krishna. From whichever angle or perspective you see him, you will find that he is complete and perfect in every way.
Excerpts from a Q&A with Sri Sri Ravi Shankar: http://celebrating-silence-of-life.blogspot.in/2015/08/why-good-people-suffer.html
There are 8 fetters which bind a person to the world and as long as a person has even 1 fetter left, they can't realize God. The 8 fetters are shame, hatred, fear, caste, lineage, good conduct, grief, and secretiveness.
The significance of Sri Krishna's stealing Gopis' clothes was to free them from their last remaining fetter.
Gospel of Sri Ramakrishna / Volume 2 / At The Star Theatre (I)
A DEVOTEE: "Sir, what is the significance of Sri Krishna's stealing the gopis' clothes?"
MASTER: "There are eight fetters that bind a person to the world. The gopis were free from all but one: shame. Therefore Krishna freed them from that one, too, by taking away their clothes. On attaining God one gets rid of all fetters.