The near years are years that weren't too long ago. They're the recent years.

Try to remember that 近年 is for the recent past (unlike 近日, which is for the near future). It's got a somewhat formal sound, so you'll more likely hear it in the news or a presentation than in casual conversation.

This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.