An infinitive can act as a subject or object. In "I want to dance", the infinitive "to dance" is the direct object that represents the thing that I want. However, that's not the only way that an infinitive can act.
Infinitives can also act as general modifiers, often expressing semantics like purpose, intent and result. We can talk about things like the question to ask, the person to see, the place to go, the thing to try -- and in all of these cases a common noun is directly modified by the following infinitive.
"The year to come" is a common noun directly modified by the following infinitive. In this case, the infinitive represents something like inevitable result. The year in question will come because it must come. There are, in fact, many years to come -- infinitely many years if time itself has no end. The definite article in "the year to come" is enough to let us know that the year in question is the next year to come, the year that immediately follows the current year.
The verb "to come" shows us one reason that bare infinitives don't work well as adjectival modifiers. The bare infinitive form is "come", but so is the past-participle form. "The year come" is more likely to be interpreted as the current year -- the year that has come rather than the year that is to come. Also, the bare infinitive is the same form as a simple present-tense form: "The years come" is more likely to be interpreted as a complete independent clause, not a mere noun phrase.
Useful search topics include use of to-infinitive and infinitive of purpose intent result.