I think a strong family means that people are count-on-able... that is, you have a network of people who you can rely on for various support. You know you can call on them to watch the kids, help with the house upkeep, etc.
I think leadership from the top - you and your spouse - showing love, understanding, discussion, etc. - that you can have a disagreement but you still love each other and work it out.
Going through hard times together, working together, reflecting, growing ...
Then there's the raising of the kids within your household - teaching kids to be respectful, feel safe, smart, thoughtful - all the things.
... there's a lot, this is just off the top of my head