Bootstrapping methods are used to measure indirect influence of certains parameters in statistical analyis. In addition to Chamalla answers and links you can check also paper of Niels Blunch 2008, entitled Introduction to Structural Equation Modelling Using SPSS and Amos.
Bootstrapping is a re-sampling procedure whereby multiple sub-samples of the same size as the original sample are drawn randomly to provide data for empirical investigation of the variability of parameter estimates & indices of fit (Byrne, 2010).
Why do we need to bootstrapping in SPSS AMOS?
We bootstrap because there is an existence of multivariate non-normal data.
To add with Mr. Han Ping Fung, Bootstrapping also treat the non-normal data as normal by drawing sub samples randomly out of the originally collected samples.
This means re-sampling from the sample but with replacement. Gives very many other samples of the same size with the original sample whose sample characteristics can be compared with those of the original sample