The kanji:
以 = by
心 = heart
伝 = to communicate
心 = heart
This idiom refers to heart-to-heart communication; speaking without words.
It is often said that the typical Japanese communication style has a tendency to leave certain things unsaid, to not say every word, and to read between the lines. “i-shin-den-shin” captures the essence of this perfectly.
This is a special kind of Japaneses idiom known as a 四字熟語 (よじじゅくご、yo-ji-juku-go), or 4-character idiom. As the name suggests, these are idiomatic phrases made of 4 kanji.
They often contain a small life lesson or moral message, similar to English sayings such as “you reap what you sow” and “the early bird gets the worm”.