What is the purpose of classifying fighters? Fighters are classified by generation, as explained in this answer. Given this Wikipedia sum up, some fighters are not clearly in a defined generation, especially for 4th generation subclasses. Thus people may not agree on a list of fighters that belongs to a generation.

Some of the previous generation (generation 4, 4+, 4.5, 4++) are still actively produced (e.g. Rafale, F/A-18E/F)  while the F-22 (definitely 5th generation) is no longer in production.

Airframe designed a long time ago (e.g. the F-15, F/A-18) still receive updates that make it competitive on international market (the section about potential operator of the F/A-18 on Wikipedia give an overview for the F/A-18), even in front of 5th generation fighters (at least in Canada for the F/A-18 and the F-35)

Another capability we cannot rely on to define generation is stealth. The A-12 and more precisely its variant YF-12 was stealth supersonic aircraft with weapons (AIM-47) inside internal bays, but was not a 5th generation fighter.
Moreover, since ECM can be fitted on a fighter, this fighter expose some stealth feature.

Given those facts, it seems that since the 4th generation, knowing a fighter is classified as a specific generation does not provide information about its production year, its capabilities nor its competitivity in front of other nation's fighters.

In short, since the 4th generation, generation does not provide reliable information about capabilities, features nor designed or production year.

What information does the generation of a fighter give? How useful it is to know a fighter belongs to a specific generation?
People like to classify things, to divide them into categories.  Categorizing allows people to get an initial broad understanding of a complicated subject more quickly.  It is therefore very useful for purposes such as marketing and articles aimed for people who aren't necessarily subject matter experts.  However, classification is necessarily a crude tool that often isn't exact, leading to confusion and arguments about where the category boundaries lie.

People who are subject matter experts, such as designers of a new fighter plane, or military analysts trying to determine the capabilities of a new secret aircraft produced by other countries, presumably don't spend much time wondering into which category to put a given aircraft.  Instead they focus their time on the details of the subject, the same details that are too much information for the person trying to get the quick grasp of the complicated subject.

To answer your questions specifically, knowing the generation of a fighter gives someone a rough idea of its capabilities, and allows the person to quickly compare a given fighter aircraft to other fighter aircraft.  Knowing the generation of a fighter is useful for people who aren't experts on the subject who need a quick broad understanding of the capabilities of historic and modern fighter aircraft, and who need to know roughly where a given aircraft fits into the large picture.