When people talk about "half a sentence," they're not just counting the words in a sentence and dividing that number by two. Instead, they're speaking grammatically, and the grammatical division of sentences differs depending on the sentence's syntax.
Simple sentences can be divided into two halves: the subject and the predicate. The subject is the noun phrase that performs the main verb; the predicate is the main verb and all the other words that it governs. (See reference 1) In the sentence "The purple people-eater strode onto the beach," the subject is "the purple people-eater" -- a noun governing an adjective and an article -- and the predicate is "strode onto the beach" -- a verb governing a prepositional phrase.
Compound sentences join two simple sentences with a coordinating conjunction. Each simple sentence within that sentence could be considered half of the sentence. In the sentence "The purple people eater strode onto the beach, and sunbathers ran in terror," the two halves are "The purple people eater strode onto the beach" and "and sunbathers ran in terror."