You can use the phrase "that is" (or "that is to say") to clarify what you mean, usually when you've said something that was unclear, or something the other person might misinterpret. You could also substitute the phrase "I mean." You can put these phrases at the beginning or the end of a sentence. Either way is fine.
Here are some examples, in case they help:
"Well, it's too late to call grandma. Tonight, that is. We can call her tomorrow." (Clarifies: It's only too late to call grandma tonight. It's not "too late" to call her at some point in the future.)
"You won't be able to read it anyway. That is, unless you can read Japanese." (Clarifies: you won't be able to read it /unless/ you know how to read Japanese. If you do know how to read Japanese, then you will be able to read it.)
"Everyone was playing in the sand. All the kids, that is." (Clarifies that "everyone" only refers to all the kids, not the adults.)
In your example, the interviewer says "welcome aboard," which implies that Homer has already been accepted into the company. He then clarifies, "pending your successful completion of our training program, that is," which means that Homer will ONLY be "welcomed aboard" if he completes the training program successfully. Otherwise, he won't become part of the company.