A private iron (remember how 鉄 often has to do with railroad tracks and the like? Same goes here) is a private railway. There are a good number of these in Japan.
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.
I joined a private railway company in April.
The property values around this area of Tokyo are very high because both a private railway and a JR line are running through here.
In Tokyo, there is not only JR's "Suica" card, but another railway's "PASMO" card that you can use on private railways.