What does the following excerpt mean: “we request that you keep the source of the information secret but put no prohibition on the publication of the zimmerman telegram itself…"

It means that they are allowed to talk about it, publishing it, but they could not show what was the Zimmerman's telegram message.

"We won't tell you what they said, but trust me, IT'S BAD" considering that the Kaiser promised Mexico the lands the USA took from them in exchange for help fighting the americans. This was one great reason why USA joined the WWI against the German Forces.