大江 specifically refers to the Yangtze River (长江), which has long been China's cultural and geographic divide between 'north' and 'south'. Saying something reaches 大江南北 means it reaches everyone on both sides — essentially, the entire country.
history
Traced to 恽敬's 《上曹俪笙侍郎书》 (Qing): describing literary influence stretching 大江南北. The phrase became the standard way to say 'nationwide' in poetic or formal Chinese.
