Any word in a sentence that has a direct bearing on the verb is termed as कारकः kāraka. Literally “karaka” means the one that impels action. This is directly associated with the various cases विभक्तिः that govern the sense of nouns in a sentence. A noun in a sentence can behave as the Subject, Object, Instrument, etc. This behavior of the Noun is termed as कारकः in Sanskrit.

Since this behavior is closely associated with the case of the Noun, we say that कारकः governs the case of a Noun. Thus there is the concept of कारकः विभक्तिः = कारकविभक्तिः ।

Example
Rama goes to temple from home by car on Sunday for worship.
रामः m1/1 रविवासरे m7/1 गृहात् n5/1 प्रार्थनायै f4/1 वाहनेन n3/1 मन्दिरं n2/1 गच्छति verb iii/1 ।
m = masculine, n= neuter. 1/1 = 1st case singular.
Notice that the 6th case is not a Karaka Vibhakti, since it does not connect to the Verb, rather it connects to a Noun in the sentence.

Kāraka = Noun that connects to a Verb.
---
Includes exhaustive notes on
-Genitive
-Upapada
-Vibhakti
-Sati Saptami (Locative Absolute)
-Anabhihite (Undenoted)
with Ashtadhyayi Sutras.