_echo are harmless acknowledgments that your request has gotten through and has successfully been processed. This is a message type that you or your user may like not to be output to make the PSYC experience less verbose. Still you know something went wrong if you don't receive an _echo with the tag of your request.
Typical examples would be _echo_request_friendship to indicate that your request for friendship is in progress or _echo_alias_added that your /alias command did its job.
Also in this case the echo informs you that your message has reached the destination (in the case of Jabber this isn't exactly true, but most likely). It contains the message you sent, so client developers are encouraged to use it for displaying the user's own input. This gives the user a feeling for the latency and reliability of the infrastructure, when there is a little delay between hitting enter and seeing it on the screen.
IRC is traditionally contrary to this principle, so psyced won't send you any echoes by default. However some IRC clients are so smart, you can turn their built-in echo off. If that is the case, you can turn PSYC echoes on using +set echo on (with a + or / or whatever your command character may be).
When no echoes appear at all, you should presume that your message has not successfully reached the destination. This is quite essential in the way we communicate on PSYC, as a real error message will only be delivered to you after all retries have failed. If you turn off PSYC echoes, you will be a little less in control.. like back in your IRC days.. ;°)
See paragraph above, or see the psyced manuals on the Help:Contents page.