* Onii-chan: Means "older brother," but it's used affectionately, often by younger sisters (or sometimes even close female friends) towards their older brother or a male figure they're close to. It implies a cute, slightly childish tone.
* Onee-chan: Means "older sister," but is used similarly affectionately, often by younger brothers (or sometimes close male friends) towards their older sister or a female figure they're close to. It also implies a cute, slightly childish tone.
You can't simply translate them to "older brother" or "older sister" in English because it loses the affectionate and informal nature. The closest you could get would be something like:
* Onii-chan: "Big bro," "Brother," "Oppa" (Korean equivalent, but it's still not exactly the same)
* Onee-chan: "Big sis," "Sister," "Unni" (Korean equivalent, again, not a perfect match)
The best way to convey the meaning is to explain the context and the affectionate tone.