Case equality.

The #=== method is used in a case ... when ... end expression.

For example, this code:

case value
when x
  # something when x
when y
  # something when y
end

Is equivalent to this code:

if x === value
  # something when x
elsif y === value
  # something when y
end

Object simply implements #=== by invoking ==, but subclasses (notably Regex) can override it to provide meaningful case-equality semantics.