Latent class analysis (LCA) typically uses cross-sectional data to identify subgroups at a single time point; in this sense we think of class membership as being static. Latent transition analysis (LTA) is an extension of LCA used with longitudinal data where individuals transition between latent classes over time; in this sense we think of class membership as being dynamic and class membership represents a developmental stage. In LTA, development is represented as movement through the stages over time and the technique is particularly well-suited to testing stage-sequential developmental theories (e.g., the transtheoretical model); different individuals may take different paths through the stages.
A latent transition is movement from one latent subgroup to another over time. Sometimes, particularly in older literature, we refer to the subgroups as statuses rather than classes to help maintain the distinction between cross-sectional and longitudinal studies. LTA enables researchers to estimate how membership in the subgroups changes over time. In order to perform LTA, you must have longitudinal data.