This is the 12500th most frequent Russian word.
ковра
"Ковра" is the genitive singular or accusative plural form of "ковёр," meaning "carpet" or "rug" in English.
Here, 'ковра' is in the genitive case because it defines the edge (края) as belonging to or being part of the carpet.
С края ковра торчала маленькая ниточка.
A small thread was sticking out from the edge of the carpet.
The word 'ковра' here is used to denote the object 'carpet' in its genitive case form, which is part of a prepositional construction indicating location (on the carpet) with the preposition 'на' suggesting position.
Кошка лежит на ковре возле камина.
The cat is lying on the carpet near the fireplace.
In this sentence, 'ковра' is used in the genitive case to express possession or relation, showing that the color is related to the carpet.