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.
日本指折りの名店だ。
It's one of the top restaurants in Japan.
彼は業界指折りの実力者だ。
He is one of the leading figures in the industry.
世界でも指折りの技術力を持つ企業だ。
It's a company with technological capabilities among the best in the world.
2.
counting on one's fingers
The literal act of counting by folding fingers, often while eagerly anticipating something.
旅行の日を指折り数えて待っている。
I'm counting the days on my fingers, waiting for the trip.
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.