The problem with defining the term "extremist political organization" is that it is by nature one applied only in the second or third person. In other words, the word "extremism" is one we do not use to describe ourselves but only use to denigrate the beliefs of people whose ideologies or actions differ from our own. Also, what is considered "extremist" in one place or period might be regarded as normal in another place and period. For example, the extremist colonial rabble that rebelled against the British Empire are now admired by many as the Founding Fathers of the United States. Early Christians, now revered by some as founders of a major world religion, were once considered atheists because of their refusal to participate in official cults, religious extremists, and generally barbaric.
It is important to note that the winners write the histories, and thus construct themselves as "moderate" and their opponents as "extremist".
In today's media, the term extremist is usually used to refer to people whose ideological positions and political actions are at odds with the social, political, or religious norms of the countries in which they are situated. For example, in China, human rights activists are condemned as "extremists" and in Putin's Russia, advocates of freedom of speech and free elections are denounced as extremists. In western media, the two groups most often labeled "extremist" are neo-Nazis and Islamist groups such as ISIS, which not only represent atypical political positions but often advocate or practice violent forms of rebellion or protest rather than working within existing systems for political change.
Extremist Political Organizations are organized groups of people who share the same extreme political views. Members within the extremist political organizations would deny all other political views except their own, and would take their political ideas to the very limit. Just like several other extremist groups like ISIS, extremist political organizations would often believe that violence or sinful actions are justified if they are committed for a "good" cause.