A recognizable person is someone you can identify or be immediately aware of. American tourists are often recognizable because most of them only speak English (and wear fanny packs).
Some things or people are recognizable because they stand out sharply. If you paint your car in rainbow colors, it will be recognizable all over town. Others are recognizable because you know them — you’ve seen or met them earlier. When you meet your cousin at a restaurant, she may be totally recognizable despite her new haircut and stylish clothes.