Answers are paraphrased for easy reading

[Significance of Lord's appearance on earth] If we look at the cosmos, the material world contains innumerable stars and planets, and the Earth appears very insignificant in comparison. In that context, when the Supreme Lord, Krishna, personally descends as the Personality of Godhead, does that indicate a special significance of this Earth planet? It is said that once in a day of Brahma, the Lord appears here to perform His divine pastimes (līlās). How should we understand the importance or uniqueness of this earthly planet in that light?

Category: Lord's Potencies | Speaker: CPP | Date: 2024-10-11 | Time Stamp: 41:55 | Shloka: SB 2.5.35
Answer
In the description of the Lord’s appearance, there is a very beautiful verse composed by Rupa Goswami, which is quoted early in the Chaitanya Charitamrita by Krishnadas Kaviraj Goswami. Later, in the sections describing the external reasons (bahiraṅga-kāraṇa) for the appearance of Chaitanya Mahaprabhu, he explains that for a very long time, the Lord had not bestowed a particular kind of mercy. The phrase indicates that this gift had not been given for many ages. To understand how long that is, he explains the structure of time:

The four yugas—Satya, Treta, Dvapara, and Kali—together form one mahā-yuga
71–74 such mahā-yugas make one manvantara, ruled by a Manu
There are 14 such Manus in one day of Brahma
Altogether, a day of Brahma consists of about 1,000 mahā-yugas

Now the key point:
Krishna does not appear in every Dvapara-yuga. He appears only once in a day of Brahma, specifically in a particular cycle (traditionally understood as the 28th Dvapara of the 7th manvantara). Immediately following that appearance, in the Kali-yuga of the same cycle, He appears again as Chaitanya Mahaprabhu. So when we ask, “Why is Earth special?”—this is the answer.

Out of thousands of yuga cycles:
The Lord personally appears only once. Most of the time, the universe is managed by His expansions and avatāras. Direct involvement is extremely rare

An analogy helps: In a government, the Prime Minister does not personally manage every department—like prisons, for example. Those are handled by appointed officials. Similarly, the material world is compared to a kind of reformatory place for conditioned souls, and its management is handled by empowered beings—expansions of the Lord such as Mahāviṣnu and others. But still, once in a day of Brahma, the Lord Himself comes.

This shows:
how rare His personal appearance is
how special this Earth becomes during that time
and, within Earth, how especially sacred places like Bharata Varsha and Vrindavan are considered

So this is the deeper understanding:
the Lord’s appearance is not ordinary—it is a rare, intentional descent, carrying both internal and external purposes, beautifully explained in the teachings of the ācāryas.