A simple sentence (sometimes called an independent clause) is a sentence that contains one subject and one verb. It has only one clause. It must also express a complete thought. This follows the rules of syntax in English grammar.
Length
A simple sentence is not defined by how short it is. A simple sentences is often short and uncomplicated. But it is not limited by the number of words used to express the thought. For example:
"Bill reads". This is a simple sentence. "Bill" is the subject and "reads" is the action (verb).
"Being an English teacher with a penchant for syntactical complexity, I love to read simple sentences upon getting up and before going to bed." This is still a simple sentence even though it uses more words.
Simple or dependent?
A simple sentence or independent clause is one that has a meaning to a reader or listener. If the sentence does not complete the thought, it may be a dependent clause. A dependent clause is one that does not express a complete thought. By itself it is a sentence fragment. It may look like a simple sentence, but it will not make sense on its own.
"Bill reads". Again, a simple sentence. Bill (a noun for a subject) reads (the action that completes the thought).
"Because Bill wants to learn more." What happens because Bill wants to learn more? We do not know, so that is not a sentence. It is a dependent clause.