What is the purpose of "!" and "?" at the end of method names?

Question mark indicates that the method returns boolean. Already answered here:

What does the question mark operator mean in Ruby?

The bang indicates that the method acts on the object itself. Already answered here:

Why are exclamation marks used in Ruby methods?

It's "just sugarcoating" for readability, but they do have common meanings:

• Methods ending in ! perform some permanent or potentially dangerous change; for example:
  • Enumerable#sort returns a sorted version of the object while Enumerable#sort! sorts it in place.
  • In Rails, ActiveRecord::Base#save returns false if saving failed, while ActiveRecord::Base#save! raises an exception.
  • Kernel::exit causes a script to exit, while Kernel::exit! does so immediately, bypassing any exit handlers.
• Methods ending in ? return a boolean, which makes the code flow even more intuitively like a sentence — if number.zero? reads like "if the number is zero", but if number.zero just looks weird.

In your example, name.reverse evaluates to a reversed string, but only after the name.reverse! line does the name variable actually contain the reversed name. name.is_binary_data? looks like "is name binary data?".

In Ruby the ? means that the method is going to return a boolean and the ! modifies the object it was called on. They are there to improve readability when looking at the code.

In contrast to the – I suppose – majority of programming languages ...

Ruby, methods are allowed to end with question marks or exclamation marks.

By convention, methods that answer questions (i.e. Array#empty? returns true if the receiver is empty) end in question marks.

Potentially “dangerous” methods (ie methods that modify self or the arguments, exit! etc.) by convention end with exclamation marks.

From: http://www.ruby-lang.org/en/documentation/ruby-from-other-languages/, Section Funny method names