The formation of amyloid fibrils and oligomers is a hallmark of several neurodegenerative disorders, including Alzheimer's disease (AD), and contributes to the disease pathway. To progress our understanding of these diseases at a molecular level, it is crucial to determine the mechanisms and rates of amyloid formation and replication. In the context of AD, the self-replication of aggregates of the Aβ42 peptide by secondary nucleation, leading to the formation of new aggregates on the surfaces of existing ones, is a major source of both new fibrils and smaller toxic oligomeric species. However, the core mechanistic determinants, including the presence of intermediates, as well as the role of heterogeneities in the fibril population, are challenging to determine from bulk aggregation measurements. Here, we obtain such information by monitoring directly the time evolution of individual fibrils by TIRF microscopy. Crucially, essentially all aggregates have the ability to self-replicate via secondary nucleation, and the amplification of the aggregate concentration cannot be explained by a small fraction of "superspreader" fibrils. We observe that secondary nucleation is a catalytic multistep process involving the attachment of soluble species to the fibril surface, followed by conversion/detachment to yield a new fibril in solution. Furthermore, we find that fibrils formed by secondary nucleation resemble the parent fibril population. This detailed level of mechanistic insights into aggregate self-replication is key in the rational design of potential inhibitors of this process.