Keep learning sessions short and fun. The first rule of teaching your 2-year-old the countries on a map (or teaching him anything, for that matter) is to keep learning sessions brief and enjoyable. Two-year-olds love to play, so if you can make map learning into a game, he will love it. Enjoy pointing at countries, saying their names, asking him where certain countries are, and asking him the name of countries as you point to them. When he loses interest, it is time to stop learning for the day. You can always pick up later where you left off.
Use a map where each country is colored a bold color, different from the surrounding countries. The map you use to teach your 2-year-old the countries of a continent or of the whole world should not be a detailed map showing all the different physical features of earth, with natural colors like browns, blues and greens. Instead, the best kind of map for a child learning country names is a map where each country is a different bright color --- red, blue, yellow, etc. Bright colors help the child to distinguish the countries easily, and to learn their shapes and their location in relation to one another.
Go in order. Before you start randomly quizzing your 2-year-old on the countries on a map, teach him the countries in order. A reasonable order to go in is top to bottom, left to right; this order in learning items of any sort (including countries on a map) helps prepare a child for the order in which he will read words once he learns to read. So, for example, if you are teaching your child the countries of Africa, show him a large, colorful map of the continent of Africa; point to the leftmost, uppermost country and tell him, "This country is Morocco! Can you say 'Morocco'? Good. Now, which country is this?" Going in order, do just a few countries and let your child get used to their names before adding more.
Incorporate other elements than just a map. While you are teaching your toddler the countries on a map, this is a great time to introduce him to new cultures and the people who live around the world. If you can find pictures of people and interesting scenes of the countries whose names and locations you are learning, your 2-year-old will be learning much more than just how to read a map and name the countries in the world. Check out children's books from your local public library that highlight life in various countries you are teaching your toddler; then, as he learns the country names on the map, he will be able to make a connection between the map and the realities of these countries and their cultures.