How to work with Maps in Kotlin

The reason for your confusion is that plus is not a mutating operator, meaning that it works on (read-only) Map, but does not change the instance itself. This is the signature:

operator fun <K, V> Map<out K, V>.plus(pair: Pair<K, V>): Map<K, V>

What you want is a mutating operator set, defined on MutableMap:

operator fun <K, V> MutableMap<K, V>.set(key: K, value: V)

So your code may be rewritten (with some additional enhancements):

class Person(var name: String, var lastName: String, var age: Int)

val nameTable = mutableMapOf<String, Person>()
val example = Person("Josh", "Cohen", 24)

fun main (args: Array<String>) {
    nameTable["person1"] = example

    for((key, value) in nameTable){
        println(value.age)
    }
}