Simply put, an infinite verb is one that does not change based on the subject with which it corresponds. For example, the verb "playing" is considered an infinite verb. A person could say he is playing, they are playing, I am playing, or we were playing, and the verb remains the same. A verb such as "play" does not remain the same, however, and is not considered an infinite verb. It changes based on the subject with which it is used: we play, they play, he plays, and she plays.
In some languages, verb forms change depending on the subject to which the verb is related. For example, a person may say something like, "I like fish." It would not be correct, however, for him to say, "He like fish." This is due to the fact that the word "like" is a finite verb, and the correct way of making this statement is to say, "he likes fish." An infinite verb, however, is the opposite of a finite verb in that it does not change forms based on the subject to which it corresponds. A person can say he is loving, they are loving, we are loving, and I am loving without changing the verb form.
Often, infinite verbs appear with the word "to." For example, "to build" is an infinite verb. A person may say he wants to build a house, she wants to build a house, they want to build a house, or we want to build a house. In contrast, the word build by itself is not considered an infinite verb. An individual may say I build, you build, or we build, but when he needs to use she or he as the subject, the form of the verb has to change to she builds or he builds, so this particular verb is actually finite.
Even when a person doesn't know right away whether a verb is finite or infinite, he can usually discover which category it fits into just by trying it out in speech or writing. For example, he may start with a word such as "made" and use it with several different subjects in order to determine whether it is finite or infinite. If he determines that he can not use the word with various subjects without changing it, it is not an infinite verb. This may only prove helpful for people who are familiar with the language in question, however. Language students may have difficulty noting the difference, as they may not easily determine which use is correct.