1.
leading; prominent; one of the best; top-ranking
Among the very best in a group or field. The image is of counting the top items on one's fingers — so few that they can be counted on one hand.
Sense 1 uses the pattern 〜指折りの: 日本指折りの (one of Japan's best), 世界指折りの (among the world's best). Sense 2 uses the pattern 指折り数える (to count on one's fingers), typically while eagerly awaiting something. Both senses derive from the image of folding fingers to count — the first implies something so exceptional it can be counted among the select few.