Suspensions are units in a Weibull life test are units that are still functional or are failed by different failure mode. In a weibull analysis all the units in the analysis must have the same failure mode. If different failure modes are not suspended the weibull line fit will be poor. For more information of different failure modes in one plot see here. Units that are suspended will have in influence on the weibull curve.
To get some understanding of the influence look at the weibull graphs below. In the table suspended units are marked gray.