When you 'hold a conversation' or are able to 'maintain a conversation' it means to be able to carry out a conversation effectively enabling the discussion to continue without any awkward silences, offering insights, building on what the other person is saying and contributing to a conversation in a meaningful way.

1. Students often test their language skills by holding a conversation with a native speaker.
2. He didn't get the job as he was unable to maintain a conversation in English.

1. I felt that the candidate excelled in knowing about technical aspects of the job but when it came to soft skills, such as holding a conversation, he struggled.
2. I find it very difficult to maintain a conversation in French over the phone. I find I often mishear what the other person is saying.