To solve the question regarding the process of inducing the formation of vegetative organs from cells or tissues in plant tissue culture, we must understand the definition and application of the given terms.

1. Somatic Embryogenesis: This is the process by which plant somatic cells develop into embryos, eventually forming a whole plant. This is not limited to specific organs.
2. Dedifferentiation: This refers to the ability of a mature plant cell to revert to a less specialized state, often a precursor to both organogenesis and somatic embryogenesis. However, it itself does not directly pertain to forming organs.
3. Organogenesis: This is the process of organ formation from explant tissues. It is specifically the formation of shoot, root, or other vegetative organs from plant tissues employed in tissue culture. Thus, this is the correct answer to the question.
4. Somatic Hybridization: This involves the fusion of protoplasts from different plant species (or varieties) to create hybrid cells and plants. It is not related to direct organ formation in tissue culture.

Based on the explanations, the correct answer is Organogenesis because it specifically refers to the formation of new organs rather than entire plants or hybrid plants.