In short equator is defined as the line passing from the center of earth which divides the entire planet into two parts , northern hemisphere and southern hemisphere. for more information you can refer to  wikipedia

so the question is which countries are  most nearest to the equator.

There are total 14 countries nearest to the line of equator or some of them are passing through the equator line.

Kenya
Somalia
Indian Ocean
Ecuador
Pacific Ocean
south of Baker Island
São Tomé and Príncipe     Ilhéu das Rolas
Atlantic Ocean     Gulf of Guinea
Republic of the Congo
0Democratic Republic of the Congo
Uganda
0Lake
Ecuador
Colombia
Brazil
Karimata Strait
Indonesia
Makassar Strait
Indonesia
Gulf of Tomini
Molucca Sea
Halmahera Sea
south of Aranuka

hope you will find this information interesting , this is updated and knowledgeable fact.