What does to_proc method mean?

I am learning rails and following this thread. I am stuck with the to_proc method. I consider symbols only as alternatives to strings (they are like strings but cheaper in terms of memory). If there is anything else I am missing for symbols, then please tell me. Please explain in simple way what to_proc means and what it is used for.

Some methods take a block, and this pattern frequently appears for a block:

{|x| x.foo}

and people would like to write that in a more concise way. In order to do that they use a combination of: a symbol, the method Symbol#to_proc, implicit class casting, and & operator. If you put & in front of a Proc instance in the argument position, that will be interpreted as a block. If you combine something other than a Proc instance with &, then implicit class casting will try to convert that to a Proc instance using to_proc method defined on that object if there is any. In case of a Symbol instance, to_proc works in this way:

:foo.to_proc # => ->x{x.foo}

For example, suppose you write:

bar(&:foo)

The & operator is combined with :foo, which is not a Proc instance, so implicit class cast applies Symbol#to_proc to it, which gives ->x{x.foo}. The & now applies to this and is interpreted as a block, which gives:

bar{|x| x.foo}

The easiest way to explain this is with some examples.

(1..3).collect(&:to_s)  #=> ["1", "2", "3"]

Is the same as:

(1..3).collect {|num| num.to_s}  #=> ["1", "2", "3"]

and

[1,2,3].collect(&:succ)  #=> [2, 3, 4]

Is the same as:

[1,2,3].collect {|num| num.succ}  #=> [2, 3, 4]

to_proc returns a Proc object which responds to the given method by symbol. So in the third case, the array [1,2,3] calls its collect method and. succ is method defined by class Array. So this parameter is a short hand way of saying collect each element in the array and return its successor and from that create a new array which results in [2,3,4]. The symbol :succ is being converted to a Proc object so it call the Array's succ method.