A Jihadi is someone who follows Muhammad's example.
A Jihadi is someone who follows the teachings of Islam strictly.
There are many Muslims around the world who are not strict about it, just as there are people who say they are Buddhist or Christian who are casual about it, who don't meditate or pray, who don't go to church or read scriptures or sutras. And it is lucky for us so many Muslims are lackadaisical about being a Muslim because those who are strict about Islam are dangerous to everyone who is not a Muslim.
This is not bigoted. This is not "hate-speech." Muhammad lived in a tough time, and his violent ways of winning converts and wealth may have been common in his time, but unfortunately in the principle Islamic holy book, the Qur'an, it says over seventy times that a good Muslim should follow Muhammad's example. It is very clear on that point. And his example was intolerant and violent to non-Muslims.
So a Jihadi is someone who believes the Qur'an means what it says: That the way to Paradise, the way to win the approval of Allah, is to establish Shari'a in every country of the world, and to use violence if necessary. Shari'a subjugates all non-Muslims, giving them a second-class status called "Dhimmi."
The goal of establishing worldwide Islamic domination is a Jihadi's most important purpose, and his whole life is devoted to it. Muhammad said living in a monastery was a lazy coward's way of showing your devotion to Allah. Actions speak louder than words. A true believer should risk his life, invest his money, and spend his time working to fulfill the goal Allah has given him: To never rest until the whole world submits to Allah. The process Muhammad gave his followers to fulfill this goal is jihad.
Here's something from Answers.com on "Jihadi:"
Jihadi is a political neologism (new word or expression) referring to an individual who participates in advancing jihad politically or militarily, most often referring to the people directly engaged in Islamic terrorism or supporting it. The roots of the term lie with the terrorists themselves, as they publicly adopted it as evidenced by many public speeches and text by terrorists such as Osama Bin Laden. Hence, the term was not placed on them by others...
The correct Arabic term for one who engages in jihad is "Mujahid" (plural is Mujahideen). The formation of "Jihadi" from "jihad" may be based on the example of the word-final-i which refers to place of origin such as "Saudi", "Pakistani", "Afghani," "Israeli," etc.