The standard deviation describes how much on average the scores differ from the population mean. So, the larger the standard deviation, the more respondents tend to disagree about a particular item.
Once you start thinking about whether respondents agree or disagree about items, you often start thinking about whether there are segments of people who are quite different in their patterns of MaxDiff scores from other segments of people. That's what the Latent Class score estimation deals with. There is some good documentation on the latent class procedures within the Lighthouse Studio documentation. I'm assuming you're using Lighthouse Studio software.