This word has the generic connotation of "good/cool" and can be used in almost any context that those two words can be used. It can be used less emphatically as a passing comment such as "Terminaste tu tarea? Chevere." (You finished your work? Good." Or it can be said more emphatically to have the connotation of "great/awesome" such as "Ganaste el juego? Chevere!" (You won the game? Great!). It is also very common to use the very emphatic phrase "Que chevere!" to mean "how great!" or "how awesome!".

In terms of its origins, it derives from the African which means that with all due respect to the Venezuelans and Puerto Ricans that have already posted (I am Puerto Rican), the word was almost certainly popularized first in CUBA where Afro-Caribbean culture was strongest. For example, the word was already being used in very early rumba/mambo songs (e.g. Guaguanco Callejero) for as long as we have had recorded evidence. Cuba was the first major exporter of Afro-Caribbean culture to the Spanish-speaking world (and indeed to the entire world), so it was from Mambo songs played on the radio that the word probably disseminated into the popular culture.

The reason why the word may be associated with Puerto Rico more now is that since the 60's - after Cuba was cut off from the world - Puerto Rico became the main proponent of Afro-Caribbean culture (and has itself been surpassed in the last decade or two by the Dominican Republic). Sorry Venezuelans, but to my knowledge Venezuela has never been a major exporter of Afro-Caribbean culture to the rest of the world.
Ganaste el juego? Chevere!
by lmalave April 9, 2008
A popular expression in use by Cubans, Puerto Ricans, Venezuelans and other Latinos as an affirmative, acclamation
of approval.
When listening to music, checking out the opposite sex or delighting in some pleasurable experience, one may make reference to said experience with, "chevere"!

Cuando bailando con Maria, Carlos dice, bamboleate guapa, mientras pensando, chevere!
by Dr. Figueroa November 3, 2006
its slang for 'cool' in spanish.
Toda Mi Gente Estan En El Party
Por Detras Guayando Las Shortys
Smoking Weed, Drinkin Hipnotic
Latinos, Mi Estilo, And Everything Is Chevere
by s3xy latina November 21, 2006
This word came to Puerto Rico through the Venezuelan TV novelas (soap operas) that were popular in the '60 and 70. It brought to Venezuelan by the African slaves of the West Coast country of Nigeria. It is from the Ibo tribe and the literal translation from "che ebere" is god's mercy.
That's chevere, or chuchi. Chuchi seems to be derived from chevere?
by NOt afraid to know the truth November 30, 2007
"Cool" in Spanish, but mostly used in Puerto Rico.
I just got an A on my exam. ¡Qué chévere!
by miguelito March 10, 2005
Palabra calificativa usada por los caleños (Cali, Colombia) para referirse a una posición positiva sobre una situación agradable, o con la que sienten empatía.
Sería chevere ir al estadio.

Que chevere que conseguiste un nuevo trabajo.

Estuvo muy chevere la fiesta.
by melissaram October 21, 2013
Anything you like, you can say que chevere. Kinda like cool.
by Jim February 27, 2005