Remember the secondary meaning of 本 being "origin"? That technically makes this sun origin. Does that sound familiar? Japan is known as the "land of the rising sun", which is why this means Japan!

This is a jukugo word, which usually means on'yomi readings from the kanji. The 本 is read just how you learned it, but the 日 reading is sort of an exception here, so here's a mnemonic to help you:

You've finally arrived in Japan and immediately fall down on your knees (に). After two excruciatingly long flights, you've finally made it. You're here. This is Japan. Now get up off your knees, people are starting to stare.