Someone is "speechless" if they are so overcome with emotion that they can't talk. Usually, that emotion is shock or surprise, sometimes sadness or anger, but if you are so emotional that you cannot think of the right words to say, you can just say "I am speechless." Or even just "Speechless." (You can also say that about someone else. e.g. "After Ted found out that Sally was really an alien from the planet Saturn here to colonize the earth, he was speechless and just stood silently for 10 minutes.")
Here it sounds like the person who said that was shocked (or whatever) already in the middle of a sentence when the shock happened. Or that they're the type of person who never shuts up. They're basically saying that they're very, very shocked - but they also want to keep talking. :)