The term "clause" refers to a group of words that minimally contains some type of subject and some type of verb. With respect to verb type, there are two basic kinds of clause in English: "finite clauses" and "nonfinite clauses."
A finite clause contains an explicit subject in the form of a noun phrase (for example, students, the software engineer, a computer that they purchased) or a pronoun (for example, we, she, they). In addition, the finite clause contains a "finite verb"--a verb that either expresses tense (for example, past or present) or that follows a helping verb such as can, should, or must. The following sentences are examples of finite clauses (the finite verbs are highlighted).
The design engineer changed the design of the computer.
The design engineer might change the design of the computer.
In the first sentence, the finite verb changed expresses tense, in this case, past tense. In the second sentence, the finite verb might change consists of the helping verb might followed by the basic form of the verb change. In both instances, the verbs are preceded by an explicit subject, the design engineer.
The above sentences each contain one clause and serve as independent sentences. However, a sentence can contain more than one finite verb and therefore more than one finite clause. The following sentence contains two finite verbs, suggested and should develop. The second clause, that we should develop a new product, actually occurs "inside" the first clause, serving as the object of the first finite verb, suggested.
The software engineer suggested that we should develop a new product.
Importantly, each finite clause contains a finite verb, which is preceded by an explicit subject. The subject of suggested is the software engineer, and the subject of should develop is we.
Unlike a finite clause that contains a finite verb, an "infinitive clause" contains an infinitive. An infinitive consists of the word to followed by the basic form of the verb: to go, to prepare, to procrastinate, etc. In the following sentence, the infinitive to repair comes after the finite verb tried.
The technical support specialist tried to repair the computer.
Although an infinitive always occurs in a sentence that contains, additionally, a finite verb, because the infinitive is a type of verb, it can have its own object. The object of to repair is the computer, and the sequence to repair the computer is the infinitive clause in the above sentence.
If finite verbs have explicit subjects in finite clauses, why don't nonfinite verbs such as infinitives have subjects? In fact, they do. Linguistic theory assumes that all clauses have subjects, both finite and nonfinite. However, in most nonfinite clauses, the subject is "invisible" or understood; it is a mental placeholder before the nonfinite verb to which users of a language assign a "logical subject."
In the sentences below, we can use a symbol(§) to represent the position of the logical subject before each infinitive.
The technical support specialist tried § to repair the computer.
The engineer asked the technician § to diagnose the problem.
In the first sentence, we understand the technical support specialist to be both the explicit subject of the finite verb tried and the logical subject of the infinitive to repair. That is, the technical support specialist is understood to be the "doer" of both the trying and the repairing. For that reason, we use the separate symbol § to indicate the doer of the repairing.
In the second sentence, the same element does not serve as the subject of the finite verb and the subject of the infinitive. The explicit subject of the finite verb asked is the engineer, and the logical, or understood, subject of to diagnose is the technician, which also serves as the object of the verb asked. In other words, the technician receives the asking and is also expected to do the diagnosing. We therefore assume that there are two separate elements representing these two functions: the technician is the explicit object of asked, and § is the (invisible) logical subject of to diagnose, which we interpret to be the technician.
The interpretation of the logical subjects of infinitives is not arbitrary. It is guided by the inherent properties of specific verbs and by other properties of sentence structure, as will be shown further on.