Non-response bias occurs in statistical surveys if the answers of respondents differ from the potential answers of those who did not answer.
If one selects a sample of 1000 managers in a field and polls them about their workload, the managers with a high workload may not answer the survey because they do not have enough time to answer it, and/or those with a low workload may decline to respond for fear that their supervisors or colleagues will perceive them as unnecessary (either immediately, if the survey is non-anonymous, or in the future, should their anonymity be compromised by collusion, "leaks," insufficient procedural precautions, or data-security breaches). Therefore, non-response bias may make the measured value for the workload too low, too high, or, if the effects of the above biases happen to offset each other, "right for the wrong reasons."
There are different ways to test for non-response bias. In e-mail surveys some values are already known from all potential participants (e.g. age, branch of the firm, ...) and can be compared to the values that prevail in the subgroup of those who answered. If there is no significant difference this is an indicator that there might be no non-response bias.
In e-mail surveys those who didn't answer can also systematically be phoned and a small number of survey questions can be asked. If their answers don't differ significantly from those who answered the survey, there might be no non-response bias. This technique is sometimes called non-response follow-up.
Generally speaking, the lower the response rate, the greater the likelihood of a non-response bias in play.
Related terminology 
Response bias is not the opposite of "non-response bias" but instead relates to a possible tendency of respondents to give an answer a) of which they believe that the questioner, or society in general, might approve or b) that they perceive would help yield a result that would tend to promote some desired goal of their own.
- Special issue of Public Opinion Quarterly (Volume 70, Issue 5) about "Nonresponse Bias in Household Surveys": http://poq.oxfordjournals.org/content/70/5.toc