Jaco-Shalen-Johannson torus decomposition

The Jaco-Shalen-Johannson torus decomposition is a topological[?] construct defined as follows:

"Irreducible orientable compact 3-manifolds have a canonical (up to isotopy) minimal collection of disjointly embedded incompressible tori[?] such that each component of the 3-manifold removed by the tori is either atoroidal[?] or Seifert-fibered[?]"

See Thurston's conjecture for relevance.