The Makkan Chapters are those which were revealed in Makkah. This refers to everything revealed before the Migration to Madinah, even if the verse was revealed while the Prophet (ﷺ) was outside of the city of Makkah.
The Makkan Chapters are those which were sent down to address the people of Makkah. The Makkan verses are distinguished by strength and sternness in addressing the people because the people would turn away and show arrogance, so this suited their state. Read for example Al-Mudaththir and Al-Qamar. The Makkan verses are usually shorter, and are strong with their argument against the deniers (i.e. the idolators) and are appropriate to their condition at the time. Read At-Toor as an example.