Quasars are QUASi-stellAR radio sources. That means they look like stars but are very active young galaxies producing radio signals. Well, this was their definition when they were first discovered. Later it came to be known that there are many different types of quasars of which many are radio quiet. Also, it is known that some young stars are radio loud. So, what are these objects?
Stars are small objects in the sky and they appear as points. But galaxies are typically 
stars in one cluster and thus appear to be slightly elongated or spreadout objects. Our galaxy, the Milkyway
is spiral in shape while there are some that have elliptical
shape or even some others without any shape. Most of the irregular galaxies, as they are called had a shape at some time in the past. They lost their shape mostly due to the interaction with black holes or collision with other galaxies.
When astronomers say that an objects appears like a star, what they mean is that they look point like or unresolved. Why do quasars look like stars? One reason is that they are very far away. The second reason is that their centre nucleus is so bright that it outshines the rest of the galaxy. Like we see only the headlight of an approaching car in a dark night, only the nucleus of the galaxy will become visible to us. This makes quasars look like stars.
All right, now what is the source of radio signals from these objects? The brightness of the nucleus of the galaxies confirms that they are very actively consuming energy. Thus such galattic nucleus are now called AGNs or Active Galattic Nucleus. Where from do they get so much of energy?
The first quasar was discovered in 1963. It is the brightest quasar that can be seen through an ordinary telescope. Located in the constellation Virgo, it is called 3C 273. The brightness of 3C 273 is about 
times that of our sun and is about 10 times that of our whole galaxy! You can now imagine why astronomers call them AGNs.
Lets come back. Where do all this energy come from? Powerful telescopes have enabled astronomers see the host galaxy that house the quasars. The energy comes from the host galaxy. Those galaxies are believed to have a supermassive blackhole at their centre. Through a process called accretion the gravity of the supermassive blackhole pulls surrounding gas and objects towards the centre of the galaxy. This produces lot of heating and burning which makes the centre of the galaxy very bright.
Well, this all sounds like a horror story. But, how do we know that the story is true? Astronomers do this by studying the spectra of the quasars. We know that matter emits energy spectra when heated. Like figureprints, each molecule has its own characteristic energy spectra that makes it easy to identify them. The spectra of a quasar is identical to the spectra of a accretion disc (continouos and broad emission lines) composing mostly of hydrogen, oxygen, carbon, magnitium etc that are being accelerated close to the speed of light. It can happen only when there is a blackhole that is pulling them with unimaginable gravitational pull. This makes our story rational.