What does &. (ampersand dot) mean in Ruby?

It is called the Safe Navigation Operator. Introduced in Ruby 2.3.0, it lets you call methods on objects without worrying that the object may be nil(Avoiding an undefined method for nil:NilClass error), similar to the try method in Rails.

So you can write

@person&.spouse&.name

instead of

@person.spouse.name if @person && @person.spouse

From the Docs:

my_object.my_method

This sends the my_method message to my_object. Any
object can be a receiver but depending on the method’s visibility
sending a message may raise a NoMethodError.

You may use &. to designate a receiver, then my_method is not invoked
and the result is nil when the receiver is nil. In that case, the
arguments of my_method are not evaluated.