1000 ri; a long distance
Often used figuratively to emphasize great distance or vastness. The ri is an old unit of length (about 3.9 km), so 1000 ri is roughly 3900 km, but the word is used for any very long distance.
A journey of a thousand miles begins with a single step.
He ran a long distance to return to his hometown.
I live in a place a thousand ri away from my hometown.
He was delighted by a letter that arrived from a distant place a thousand ri away.
遠距離 is the modern, literal word for 'long distance' used in everyday contexts like 遠距離恋愛, whereas 千里 is a classical, poetic way to express vast distance.
近距離 means a short distance, the opposite of the vast distance implied by 千里.
From Chinese 千里 (qiānlǐ), literally 'thousand li'. The li (里) is a traditional Chinese unit of distance, adopted in Japan as ri. The expression is used proverbially to indicate a very long distance.