Linked from
The 15 pages that link to Dispersion relation, each with the reason it gives.
Angular frequencyRelated: It determines how angular frequency varies across wave modes.
Phase velocityRelated: Its slope from the origin gives phase velocity at each wavenumber.
WavenumberRelated: It specifies how temporal oscillation depends on spatial repetition in a medium.
QuasiparticleRelated: It specifies how a quasiparticle's energy varies with momentum.
Wave vectorRelated: It maps which frequencies are allowed for each wave vector in a medium.