It is a "rice ball", usually with some kind of meat inside and wrapped in seaweed (similar to sushi). Unlike sushi though, which you hold and eat with chopsticks, an onigiri is made to hold in the hand.
The o- is an honorific prefix. It is used to give respect to an object or person, and is done with several choice words (including o-sushi). This sociolinguistic aspect of the Japanese language is imperative to understand, as some words can often sound harsh and/or insulting if the honorific prefix is omitted. See this article for a more detailed description.
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[握]{にぎ}り[寿司]{ずし} is a specific kind of sushi. An お[握]{にぎ}り is a rice ball. The word [握]{にぎ}り alone simply means "a grip or handle" (like a doorknob). They're all derived from the verb "[握]{にぎ}る", meaning "to grasp". On the second page you posted, they appear to be using "nigiri" as shorthand for "nigiri-zushi".