What is the significance and why lord Krishna driving Arjuna's chariot in Mahabharat war?
Truly he didn't fight on either on the side of Kaurvas or Pandavas he gave his celestial army (Akshauhini) to Duryodhana and became the charioteer of Arjuna without participating in the battle such is Lord's glory.
It is partially explained here:— Why didn't Krishna take a more active part in Battle of Kurukshetra in Mahabharata?
but whole answer is here:—
"Vaisampayana continued, 'Thus addressed by Krishna, Dhananjaya the son of Kunti selected Kesava who was not to fight on the battle-field, even Narayana himself, the slayer of foes, increate, born among men at his own will,--the foremost of all Kshatriyas and above all the gods and the Danavas . And Duryodhana selected for himself that entire army (composed of the Narayanas). And, O descendant of Bharata, having obtained those troops numbering thousands upon thousands, he was exceedingly delighted, although he knew that Krishna was not on his side. And having secured that army possessed of terrible prowess,
Duryodhana went to the son of Rohini of great strength, and explained to him, the object of his visit. The descendant of Sura in reply addressed the following words to Dhritarashtra's son, 'Thou shouldst remember, O tiger among men, all that I said at the marriage ceremony celebrated by Vitrata. O thou delighter of the race of Kuru, for thy sake I then contradicted Krishna and spoke against his opinions. And again and again I alluded to the equality of our relationship to both the parties. But Krishna did not adopt the views I then expressed; nor can I separate myself from Krishna for even a single moment. And seeing that I cannot act against Krishna even this is resolution formed by me, viz., that I will fight neither for Kunti's sons nor for you. And, O bull of the Bharatas, born as thou art in Bharata's race that is honoured by all the kings, go and fight in accordance with the rules of propriety.'
"Vaisampayana continued, 'Thus addressed, Duryodhana embraced that hero wielding a plough for his weapon of battle, and although knowing that Krishna had been taken away from his side, he yet regarded Arjuna as already vanquished. And the royal son of Dhritarashtra then went to Kritavarman. And Kritavarman gave him a body of troops numbering an Akshauhini . And surrounded by that military host, terrible to behold, the Kaurava marched forth delighting his friends. And after Duryodhana had departed, Krishna, the Creator of the world, clad in yellow attire, addressed Kiritin, saying, 'For what reason is it that you have selected me who will not fight at all?'
"Thereupon Arjuna answered, 'I question not that you are able to slay them all. I also am alone capable of slaying them, O best of men. But you are an illustrious person in the world; and this renown will accompany you. I also am a suitor for fame; therefore, you have been selected by me. It hath been always my desire to have you for driving my car. I, therefore, ask you to fulfil my desire cherished for a long time.'
"Vasudeva's son thereupon said, It beseems thee well, O Kunti's son, that thou measurest thyself with me. I will act as thy charioteer; let thy wish be fulfilled.'
"Vaisampayana continued, 'Then with a glad heart, Kunti's son, accompanied by Krishna as well as by the flower of the Dasarha race, came back to Yudhishthira.'
—The Mahabharata, Book 5: Udyoga Parva: SECTION VII