Galaxies come in a number of varieties, and what we call 'radio galaxies' host supermassive black holes which are producing huge jets of particles in opposite directions. These jets emit radio waves, which we image with our radio telescopes.
As the supermassive black hole pulls in surrounding intergalactic gas, an accretion disk is formed. This disk is very hot, radiating a tremendous amount of energy.
However, not all of this ionised gas is consumed by the black hole, and some of it is launched in a north/south direction by intense magnetic fields. This process is poorly understood, but we observe it as jets of particles. In some cases, these jets can extend for thousands or even millions of light years away from the host galaxy. When their are oriented in the right way from our perspective, it gives us spectacular images.
When a supermassive black hole has an accretion disk surrounding it, we call these systems Active Galactic Nuclei (AGN) because of their tremendous energy output. These systems can affect the evolution of the entire galaxy.
Radiative-mode AGN release most of their energy from the hot accretion disk in the form of X-Rays - they can also have radio jets releasing a smaller fraction of their energy. Jet-mode AGN don't have such a hot accretion disk, and instead release most of their energy in the form of radio jets.
A schematic diagram showing radiative-mode (a) and jet-mode (b) active galactic nuclei. Depending on their orientation, we see various perspectives from our vantage point on Earth. Diagram from Heckman & Best, 2014.
Many shapes and sizes
Sometimes the jets can twist and turn as they interact with gas outside of the galaxy. Some can leave trails behind them as the host galaxy speeds through space. The above images will take you to more detailed sources about them.