Functional style counter in Groovy

I am very new to functional programming concepts and was watching a presentation by Neil Ford in youtube. There he talks about a counter to demonstrate a piece of code without using a global state(at 20:04). Coming from Java world, I have some difficulty to understand the concept here and how the counter is incremented. Below is the relevant code

def makeCounter() {
    def very_local_variable = 0;
    return {very_local_variable += 1}
}

c1 = makeCounter()
c1()
c1()
c1()

c2 = makeCounter()
println "C1 = ${c1()}, C2 = ${c2()}"

He goes on to say that C1 = 4, and C2 = 1 will be printed. How does this happen? I am sure my lack of understanding here stems from probably a conceptual failure in how Groovy works or probably there is something general in functional languages like Groovy, Scala etc. Does a local variable within a method maintains its state until the function is called again and assigned to another variable? (A google search with "functional counter groovy| scala" brings nothing)