Groups refer to the different designs each rarity has. Each group has 7 categories of designs with different probabilities for each category.
As you can also see each design type (Armor, Chassis, Tower, Gun) has a characteristic next to it. That is because each type boosts that characteristic. The less probable a category of the design type is the more it boosts its corresponding characteristic. If you are confused take a look at the tables below!
Boost of Characteristics according to the Category of the design type (Common):
So category 7 of Body boosts your Tank's Armor by 12, category 3 of Tower boosts your Tank's Ricochet by 0.3, and so on and so forth!
Boost of Characteristics according to the Category of the design type (Rare):
As you can see Rare design types boost a characteristic more than a common one. For example, Category 1 of Gun for common Rarity props up Rate of Fire by 0.4, while in rare for 0.6.
Boost of Characteristics according to the Category of the design type (Legendary):