The subject of a sentence is the most important thing and all the other things may be dependant on it. In this case, the infinitive form "to travel" functions as the subject of the sentence because it is the main head that controls the other phrases, the modifiers which make the infinitive form mean something. It is possible to notice that when you reorganize the sentence in different forms, such as "to travel is the plan Joel has for this summer", or "travelling is Joel's plan for this summer".
In grammar, some verbs including the verb to be and other verbs such as look, like, seem or become are classified as linking verbs which means they do not express an action but describe the subject by linking this with the complement. This the case of the verb "is" (verb to be) that is the main verb in the sentence "This summer, Joel's plan is to travel". Besides this, in the case of this type of verbs, the word or words that go after the linking verb and complete the idea are called a predicate nominative. In opposition to the direct and indirect object that go after an action verb. This implies in this case, the words "to travel" that is the infinitive in the sentence are a predicate nominative because they go after a linking verb.
