Transition metals often form a type of compound known as a "coordination compound." A coordination compound occurs when one substance in a compound has a molecule (a group of two atoms bounded together) with a spare electron, and another substance in the compound adds this electron to its "electron shell." Transition metals, because they have more orbitals in their electron shells than many other elements, are often the recipient of these spare electrons from other molecules, such as water.
One important effect of being able to take an extra electron is that transition metal compounds often vary wildly in their color, and the color changes depending on what molecules or atoms are added to the compound. For example, copper (a transition metal) has a natural reddish brown color, but it is white when in a compound with a sulfate molecule (SO4). Moreover, this same compound changes to a light blue when water is added.
Transition metal compounds may or may not be drawn to a magnetic field, depending on what other substances are in the compound. A magnetic transition metal compound (also known as "paramagnetic") occurs when there are unpaired electrons in the outer shell, and thus is much more common when a transition metal is in a coordination compound. A transition metal not in a coordination compound is much less likely to be magnetic (also known as "diamagnetism").
The presence of a transition metal in a compound means that the compound is likely to have more than one oxidation state. Oxidation states are a hypothetical supposition of what an atom's bonds would look like if it was completely ionized (e.g., if it was given a completely positive or negative charge). All transition metals form compounds with positive oxidation states; copper is the only one that would be +1, with manganese potentially forming a +7.