D-orbital electrons in transition metals play a vital role in imparting their distinctive chemical and physical properties.

Transition metals are located in the central region of the periodic table, specifically within groups $3$ to $12$. They are characterized by the presence of d-orbitals, which are electron shells capable of accommodating up to $10$ electrons. The d-orbital electrons are crucial in defining the unique attributes of these metals.

One of the most notable properties influenced by d-orbital electrons is the ability of transition metals to form colored compounds. This phenomenon occurs because d-orbital electrons can absorb specific wavelengths of light, promoting an electron to a higher energy level. The light that is not absorbed is either transmitted or reflected, and this is what we perceive as color. For instance, copper sulfate appears blue because its d-orbital electrons absorb all wavelengths of light except for blue.

Another essential property of transition metals is their ability to form complex ions. This characteristic arises from the presence of vacant d-orbitals, which can accept lone pairs of electrons from other atoms or molecular groups, thereby forming coordinate bonds. This ability is crucial for various biological systems; for example, the iron in hemoglobin forms a complex ion with oxygen, facilitating its transport throughout the body.

Moreover, d-orbital electrons are responsible for the high melting and boiling points observed in transition metals. Their capacity to move freely enables the formation of metallic bonds, resulting in a robust and closely packed structure. Additionally, these electrons enhance the conductivity of transition metals, making them effective conductors of electricity and heat.

Finally, d-orbital electrons allow transition metals to exhibit variable oxidation states. This flexibility means that these metals can lose different numbers of electrons, leading to the formation of various ions. This property is critical in numerous chemical reactions, including those occurring in batteries and various industrial processes.

In conclusion, d-orbital electrons in transition metals are fundamental to their unique chemical and physical characteristics. These include the formation of colored compounds, the ability to create complex ions, variable oxidation states, and contributions to high melting and boiling points, as well as their excellent conductivity.