真意 (shin’i: real intention, true motive, true meaning) true + meaning
深意 (shin’i: deep or profound meaning) deep + meaning
心意 (shin’i: mind) heart + mind
Jim Breen doesn’t provide sample sentences for 深意 or 心意, but the following gives a good sense of how one might use 真意 (real intention, true motive, true meaning):
彼女の言葉の真意は何だろうか。
Kanojo no kotoba no shin’i wa nan darō ka.
I wonder what she means by those words?彼女 (kanojo: she) he + woman
言葉 (kotoba: word) word + fragment