Source: TW
Some historians define the period between the devolution of the shuNga empire founded by the brAhmaNa senApati of the maurya-s to rise of the gupta-s as the “period between empires”. Whether this term is right or wrong can be debated, but it is a useful placeholder for certain changes happening on the archaeological front. This characterization holds quite true in the North, where the shuNga-s devolved into local *mitra clans ruling small territories.
However, in the South, the empire continued much longer under the andhra (shAtavAhana) monarchs – hence, the purANa-s tend to place them in continuity with the northern ruling clans. However, they too followed a similar pattern of devolution into smaller principalities ruled by andhra-related clans and territories of the old andhra mAhAtalavara-s, mahAraTTi-s and mahAgrAmika-s.
In the North and the West of the subcontinent, this period of devolution was marked by the establishment of Iranic dynasties of yavana, shaka, pahAlava and kuShANa provenance, who came in from west and inner Asia. The last of these, the kuShANa, held an empire for a while, presaging the rise of the nationalist gupta-s. Hence, the period “between Empires” could be debated.
Coeval with, and particularly during the decline of the kuShANa-s, both the Northwest and the Northeast, saw the rise of powerful republics, like the yaudheya-s and lichChAvi-s. In the South, the imperial andhra-s fought the shaka-s, yavana-s and pahAlava-s, but also had marriage relationships with some of them.
We also support the view that one of these Hinduized groups of pahAlava-s gave rise to the pallava-s in the andhra country, who eventually founded an empire centered in the drAviDa country. All the above is perhaps a recap of history, which you probably learnt in your 5th standard textbook.