it's from slang, it's kind of a joke. It means, "I am like a conversation", more accurately: "I am not a human, I am a conversation which can walk (on legs) just like a human!" - i.e., everywhere I go, a conversation starts because of me so the correct sentence should really be "i am like a walking conversation". but saying it as "i am a walking conversation" makes it even more extreme of a metaphor :) 我好像一個能走步的對話，因為不管我去哪裡，我就跟別人聊天 ？？ 不知道你們怎麼說

I'm guessing that the speaker is either Latino or looks like a Latino. The fact that he might be an illegal alien living in the U.S. might start a conversation between those that think there should be harsher laws regarding illegal immigrants. The fact that he would start many conversations (and arguments) about that subject makes him a 'walking conversation.' [The irony here is that many people who look like they come from Mexico or Central America are actually U.S. citizens who's ancestors have been in the U.S. longer than many people who consider themselves 'true Americans'.]

Actually, the phrase you need to pay attention to is, "a conversation that most people are uncomfortable having". The speaker is a walking version of that, much in the way Ian has described. That is, the conversation isn't just words; the speaker embodies the concept.