What is the political reason for having colonies?
There are several political reasons a nation might want to have colonies.
The first is simple: power. When a nation founds a colony, they acquire power over a new region and the people in it. This might mean the colonizing nation lives as an upper class in the new area. It might mean taking slaves.
The second reason is related: wealth. Yes, that’s technically an economic reason, but you can’t separate these. When a nation develops considerable new wealth, it has immediate political consequences. If you find gold or silver, you can hire mercenaries. I
A third reason slides over into culture: a nation might think it has some duty or obligation to colonize an area that comes from non-political sources. Some aspects of the colonization of the Americas were religious: Christians wanted to bring their religion to new lands.
A fourth reason moves back into politics, but in a more subtle fashion. Nations found colonies to change their existing situation. This might mean starting trade, as was the case with ancient Greek colonies. It might mean gaining a place for ships to stop and restock. England used Australia as a penal colony, sending criminals (and others who disrupted society) far away, to keep the peace at home.
I assume that you are asking about political reasons why European countries would have wanted colonies in the 1600s or during the Scramble for Africa. In either case, the major political reason for this would have been to make their countries look stronger and more important.
In those days, countries were even more competitive than they are today. There were many countries who felt that they were, or should be, great powers. Because they were all in competition with one another to be seen as great powers, they all wanted colonies. A country that could take and keep colonies, they felt, was a strong country. Politically, then, they essentially needed to take colonies. If they did not have colonies, they would not be taken seriously in the international community.
Thus, the major political reason why a country would want to have colonies was so that the country would appear more powerful and so other countries would feel that it was more important than they would if it had no colonies.