Traffic Engineering (TE), simply speaking, is the possibility to send traffic from source to destination on a path that differs from the lowest-cost path calculated by routing protocols. There could be multiple reasons for using TE, such as the following:
The lowest-cost path to the destination is congested, so you can offload that path by redirecting (part of) the traffic over a different (longer) path.
The lowest-cost path has a high latency, so you redirect delay-sensitive traffic over a different path with lower latency while keeping the traffic that is not sensitive to delays over the lowest-cost path.
The lowest-cost path uses insecure (easy to eavesdrop) transmission media, so you redirect traffic requiring the highest security over different (more difficult to eavesdrop) path. Typically, optical transmission is considered more secure than transmission over microwave or copper links.
Certain applications might require multiple disjoint paths to a single destination for proper application-level redundancy failover. So, you can create multiple traffic-engineered paths for such applications. Potentially, these paths, or at least some of them, do not follow the lowest path to the destination.
Those are just a few examples of potential deployment scenarios for TE. But, there could be many more. Each service provider (SP) will have its own view of what traffic should be forwarded over paths that differ from the lowest-cost ...