how is cadmium used in nuclear reactors?

In the nuclear reactor cadmium used as a control rods. Cadmium has a high thermal neutron absorption cross section. Therefore Cadmium rods will absorb neutrons, making them unavailable to cause fission. There are also other properties that make cadmium a good control rod material.
Control rods are used in nuclear reactors to control the fission rate of plutonium and uranium. It is important to be able to control the rate at which the uranium atoms are undergoing fission. If the nuclear chain reaction is allowed to propagate unchecked, the rate of fission will increase rapidly as more and more neutrons are exhibited, resulting in a massive and nearly instantaneous release of energy and heat. In contrast, in a nuclear reactor, the rate at which the nuclear fuel undergoes fission is rigorously controlled using 'control rods' cylinders of neutron absorbing material that are inserted into the reactor core to absorb a portion of the neutrons released by the fission of the uranium-235 fuel. To initiate a chain reaction when a reactor is being started up, the control rods are partially withdrawn so that they absorb fewer neutrons; once the reactor is critical (i.e. a chain reaction is occurring), the control rods are placed slightly further into the core in order to slow the rate of fission to the required value and maintain it at that level.
In addition to nuclei that fission spontaneously, many other atomic nuclei can be induced to undergo nuclear fission by bombarding them with subatomic particles. For example, a slow-moving or 'thermal' neutron can be absorbed into the nucleus of an atom, rendering it unstable and causing it to fission instantly. Nuclei that are susceptible to this "induced nuclear fission" include uranium-233 and plutonium-239. Neutron bombardment can also be used to boost the rate of nuclear fission in nuclei that undergo this process spontaneously, such as uranium-235 (see Figure).
Looking more closely at the figure above, it becomes evident that the nuclear fission of uranium-235 exhibit more neutrons (three in this example) than it consumes (one). This suggests the possibility that the neutrons released when one uranium-235 nucleus undergoes fission can induce the fission of up to three neighbouring uranium-235 nuclei, each of which will also release neutrons as it fissions, which can interact with other uranium-235 atoms, and so on, thus creating a self-sustaining nuclear chain reaction. It is this chain reaction that provides the basis for nuclear research reactors and nuclear power, as it releases not only neutrons and fission products, but also huge quantities of energy.
Find out more on:
https://en.wikipedia.org/wiki/Control_rod
https://www.quora.com/What-property-of-cadmium-rods-make-them-useful-in-nuclear-reactors