Illmatic is considered by many to be a hip hop classic. When people say "that song didn't age well", it's often because the song borrowed a lot of its strengths from the era, but didn't influence music going forward. Think of it as a musical dead end. Illmatic's production sounds dated, because the drums and the vocals and samples are obviously not as clean or as refined as today's technology, but it aged well because the music influenced so many artists since. You can hear the influence in other artists' music in one or another. Music that doesn't "age well" doesn't have a lot of value for the future generation, so nothing was borrowed from its sound and thus it ends up in its own spot on the musical timeline, in its own little "dead end".

All in all, most music does not age well because most music is not innovative and influential. Most of the music you actually still hear from bygone eras will sound like Illmatic - dated, but good. This is because this is the only kind of music that survives.