Anonymous remailers are specific software (Reliable,Mixmaster, Freedom, Ghio..),
  running on machines operated by unpaid volunteers.
End-users may build their messages by hand,
  but will gladly turn to specific software (JBN, Pidaho, QuickSilver...)

Their purpose is to remove any link (identification) between the messages they receive and the ones they reemit.
Ensuring, if properly used, total anonymity for their users.
For the best and for the worst. (Cf: Why use Anonymous Remailers?)

The process is to remove *all* Header (with its various identification marks) from inbound messages
and to reemit an oubound message bearing a different Header (with new identification marks).
(This message will be a mail or a post via NNTP or a m2news gateway).
To fool possible traffic analysis,
  many messages may be merged and then split ('mix' technology, 28K messages)
  messages may be resequenced or delayed
  .....
Of course, no cross-reference table is created nor kept
      between inbound message-ID(s) and outbound message-ID(s).
The Body of the message received by the remailer is normally encrypted with a public-key algorithm.
It holds:
    -directives to the remailer on how to reemit the message (@, subject...)
    -the message to be reemitted on next hop

The most frequent analogy is the one with nested envelopes,
  where envelopes' inviolability (seal) means public-key encryption:

M Sender wants to send M Receiver a message without their relationship being known.
  M Sender writes his letter to M Receiver
  M Sender writes an envelope with M Receiver's address and slips the letter in it
  M Sender writes a sealed envelope with the remailer's address and slips first envelope into it.

What will the remailer do ?
  The remailer will open the envelope bearing his name (which he is the only able to unseal)
  He will send its content to the address mentioned on the internal envelope.

Of course, a rogue remailer could make the link between
    the marks on the external (sealed) envelope
    the address on the internal envelope

One will easily understand the purpose of chaining multiple remailers
   (slip the external sealed envelope into another sealed envelope sent to another remailer)
   which in turn will be slipped.....)

One should imagine that *all* remailers are compromised *and* exchange information between themselves
  to establish the link between M Sender and M Receiver.