A kernel clause is a simple, declarative clause. It has one verb, and it is affirmative and active. It is called a kernel clause because it is the basic kernel, or core, of clauses. "Kernel" is a metaphor to express the idea that all other clauses are described based on their differences to the kernel clause; this is the importance of the kernel clause. A kernel clause is unmarked in voice (it is indicative rather than passive), unmarked in mood (it is indicative), and unmarked in polarity (it is positive and not negative). In addition, a kernel clause cannot contain a gerund (such as "running"), an infinitive (such as "to go"), or an adjective. Kernel clauses can be divided into subjects and predicates, such as "Mary sang the tune again." In this clause, "Mary" is the subject, and "sang the tune again" is the predicate.
A kernel clause in grammar is a simple subject and a simple predicate forming the basis of all sentences. A kernel clause may stand alone as a simple sentence (independent clause), or it is dependent on and joins with another independent clause to form a longer, more complicated sentence.
The reason for the terminology "kernel" when referring to these clauses is that each one provides the essential elements to form a perfect sentence.
A sentence talks about somebody or something (the subject). So, the subject, either a noun or pronoun, can be likened to the "germ" of the kernel clause. It tells everybody what the sentence is about. The verb, on the other hand, tells something about the subject. The two together make a complete sentence.
Any additions to a sentence making it longer or more complex make it so that it is no longer a kernel sentence. But, within the sentence, one can still see the original kernel clause that formed its foundation.