Blocks reach outer local variables

TL;DR

A Ruby block does not open a fresh scope for variables that already exist. Because a was defined before the block, the a inside the block is the same local variable, so the assignment rebinds it to "inner" and the change is visible after the block returns.

Step by step

a = "outer"

1.times do
  a = "inner"
end

a # => "inner"

1. a = "outer" creates the local variable a in the outer scope.
2. 1.times runs the block once. When the parser reads the block body, a is already a known local, so a = "inner" does not create a block-local variable; it reassigns the outer one.
3. After the block, a still points at "inner".

The direction matters: blocks see locals from their enclosing scope, but a variable first assigned inside a block stays local to the block:

1.times do
  b = "inner only"
end

defined?(b) # => nil

Edge cases

You can force a name to be block-local, even when an outer variable with the same name exists, by declaring it after a semicolon in the block parameters:

a = "outer"

1.times do |; a|
  a = "inner"
end

a # => "outer"

Method definitions with def do not behave like blocks: a def body starts a brand-new scope and cannot see the surrounding locals at all. This closure behavior is specific to blocks, procs, and lambdas.