Our elders have always advised us to not crack knuckles of our fingers or elsewhere intentionally. What is the significance behind this?
Why it is bad is not mentioned as far as I know. But there are definitely scriptural injunctions condemning the act, particularly directed towards those who are living in the Brahmacharya Asrama of life ( i.e. a student).
Elders are obviously aware of those instructions.
He should seek to follow his teacher in rising, sitting, strolling, and smiling. 9 In the presence of his teacher, he should refrain from voiding urine or excrement, breaking wind, speaking in a loud voice, laughing, spitting, cleaning his teeth, blowing his nose, frowning, clapping, and cracking his finger joints, 10 as well as from embracing or speaking to his wife or children tenderly.
Apasthambha Dharma Sutras 2.5.8-10
More verses from the same text:
He should refrain from eating foods whose essence has been extracted; 11 standing on ashes or grain husks; 12 washing the feet by rubbing one foot with the other; placing one foot on the other; 13 swinging the feet; 14 placing one foot over the other knee; 15 making noises by striking the nails against each other; 16 cracking the finger joints without a good reason; 17 and other acts that are forbidden
Other scriptures also have similar verses.
Restrictive rules come into force from the time a person is initiated. 7 The rule of chastity has already been given. 8 He shall put wood into the sacred fire, beg his food, speak the truth, bathe–– 9 only after the beard-shaving rite, according to some––,* 10 and perform the twilight worship outside the village. 11 Controlling his speech, he should remain standing during the morning twilight worship from the time the stars are still visible until the sun comes into view, and remain seated during the evening from the time the sun is still visible until the stars come into view, 12 without ever gazing directly at the sun. 13 He should abstain from the following: eating honey and meat; wearing perfumes and necklaces; sleeping during the day; applying oil and collyrium; travelling in carriages; using shoes and umbrellas; lust, anger, greed, perplexity, and squabbling; playing musical instruments; bathing and cleaning the teeth; excitement, dancing, singing, calumny, and dangers; 14 wrapping his neck; sitting cross-legged, leaning against something, or stretching out his feet within sight of his elders; 15 spitting, laughing, yawning, and cracking his fingers;
Gautama Dharma Sutras 2.6-15
As you can see, why it is forbidden is never mentioned. Also, the injunction is applicable particularly for the students.