Active Galactic Nucleus

Most, if not all, galaxies have a supermassive black hole (SMBH) at their core. While certainly impressive enough on their own (the largest - the SMBH of NGC 4889 - has a mass of about 2.1 x 1010 solar masses and a diameter of about 20 to 124 billion kilometers), they can become even more impressive.

Large amounts of matter may orbit a SMBH in a disk (known as an accretion disk ) which heats up due to friction and releases high energy radiation, such as X-Rays. When this occurs at the centre of a galaxy, the core is referred to as an active galactic nucleus.

Active Galaxies are subdivided into many types, based on the frequency of emissions and the way in which they are emitted. Radio-loud types, such as some Quasars, Blazars and Radio Galaxies, emit energy via massive relativistic jets : shooting jets of plasma close to the speed of light. Radio-quiet types, such as LINERs, Seyfert Galaxies and some Quasars, do not emit energy via jets. More information can be found on their respective Wikipedia pages, linked above.

Examples of active galaxies include Centaurus A (Radio Galaxy), the Sombrero Galaxy (LINER),  the Einstein Cross (Quasar) and the Circinus Galaxy (Seyfert).

Concerning the habitability of an active galaxy, it is likely that they are almost as habitable as dormant galaxies. A planet would have to be very close to the SMBH to be significantly bathed in radiation (at which point, the normal radiation of the bulge stars would kill you anyway). Unless a relativistic jet is pointed straight at you (in which case, you die), there is no significant difference between active and dormant galaxies.

Worldbuilding in Practice
"The Thunatoo, a pre-space age civilisation inhabiting the Ripple Galaxy, noticed something terrifying when they observed TGC 43, an elliptical radio galaxy. They noticed that, according to advanced models on the movements of their galaxy, they would pass through the relativistic jet of TGC 43 within a million years. This would almost certainly eradicate all life in their part of the galaxy. The Thunatoo, and all life on their planet (and, indeed, in their quadrant of the galaxy), were living on borrowed time."