Definition
If you are searching for the medical jargon and psychiatric goop using classifications, Wikipedia doesn't have a half bad rendition of it. I imagine, however, if you are here, you aren't really a psychology student. Allow me to, instead, lay out my own understanding...it is essentially a mushed and portioned bipolar-schizophrenia flambe! Voila! Okay, that probably isn't too explanatory, so lets get in depth.

Schizoaffective (SZA) is always defined as a condition where symptoms of a mood disorder and symptoms of schizophrenia are both present. It can vary drastically from person to person, but the keys are major, depressed, short manias, and psychotic symptoms. Psychotic symptoms include delusions of grandeur, hallucinations, disorganized thinking and paranoid thoughts.
MayoClinic says this about it: "Psychotic features and mood disturbances may occur at the same time or may appear on and off interchangeably. The course of the schizoaffective disorder usually features cycles of severe symptoms followed by an improved outlook. To establish a diagnosis, a person must have demonstrated, at some point, delusions or hallucinations for at least two weeks without evidence of mood disorder symptoms." However, this is lax with many psychiatrists. Mental disorders can often be ridiculously hard to pin down especially if the individual isn't coughing up all the information. People may receive a diagnosis of schizoaffective disorder if they: have schizophrenia along with mood symptoms, have a mood disorder along with symptoms of schizophrenia, have both a mood disorder and schizophrenia or have a psychotic condition other than schizophrenia, plus a mood disorder. None of these are wrong diagnoses per say which is why it's difficult to pin it down specifically. Ultimately, as it's been explained to me SZA is fairly nonspecific as far as pining it to the wire. However if one is willing to work with a psychiatrist generally a combination of drugs in the category do the trick to stabilize them enough to cope with their depression or manic symptom in a manageable system.
SZA generally develops in mid to late adolescence or early adulthood, and that is when onset is most intense. SZA is more common in women than in men and has an overall more favorable outcome (prognosis) than schizophrenia. Untreated, people with schizoaffective disorder often commit suicide or may lead lonely lives and become further alienated from people and society.

Symptoms
Generally most of these are involved. Please DON'T take this opportunity to self diagnose.
* Depression (Major) - can leads to suicidal thoughts and behaviors
* Manic mood, or a sudden increase in energy and behavioral displays that are out of character
* Paranoia
* Sleep disturbance (Insomnia or Severe Oversleeping in a Depression)
* Hallucinations - this can be anything from hearing voices or music (auditory) or overt visual hallucinations such as monsters, the devil or more subtle ones such as shadowy apparitions. These hallucinations tend to worsen when the individual is intoxicated.
* Confused and unclear thinking
* Anxiety
Extras
* Irritability - Watching television or a movie can completely change the person's mood to angry or disturbed. They may quickly change their minds about their friends or family if they hear something negative being said about them, as a result they may attack or, conversely, back away from the person or group until they regain normal thoughts, which takes treatment and time.
* Thought-Processing - forming illogical or unique connections, difficulty with logical reasoning, impulsiveness and the way one perceives the world. Thus, one who suffers from schizoaffective disorder may have a different way of looking at the world. For instance he/she may believe that certain people remind him/her of certain kinds of animals. This, unfortunately, beginning as merely a uniqueness, can eventually present itself in the form of hallucinations. Impulsiveness is another aspect of a schizoaffective patient's cognitive deterioration.

As aforementioned, it tends to be difficult to diagnose since the symptoms are similar to other disorders with prominent psychotic symptoms like bipolar disorder with psychotic features, major depression with psychotic features and schizophrenia. The main difference between schizoaffective disorder and the other disorders mentioned, is that there is a baseline of psychosis during which mood episodes occur. In the other disorders there is a baseline disorder of mood during which psychosis may occur. A firm diagnosis of schizoaffective disorder thus may require a long period of observation and treatment.