Imagine a coin labeled "Relating to Another Person". On one side of the coin is Empathy, on the other is Intimacy. Empathy is when you feel and understand what another person is feeling, experiencing. Intimacy is about how you feel when your significant other is fully understanding what you are feeling and experiencing. When you feel that the other person "gets" you in that close, special way, that's Intimacy. And really good quality Intimacy is both people getting each other at the same time.
If you've ever sat at the dinner table with your kids, and they're rocking and rolling about one thing or another, and you look up into your spouse's eyes and smile to see him looking at you and smiling right back… BAM! That's an Intimate Moment to be treasured. And no sex involved!
Here's a corny mnemonic: Intimacy means 'into me you see'.
PS. You can have intimacy without sex and sex without intimacy, but sex with intimacy? Mmmmm!