There are some very good points in the other answers so far, but another thing worth noting is the change in priorities as you cross into this chapter of life. That's really the piece that non-parents often miss.
Of course, there's the outward signs, like not going out to the pub with the guysyour friends as much, but it's worth noting that that's the symptom and not the actual issue.
I remember being a young bachelor who scoffed at my older friends who got "chained down by the wife and/or kids". At the time my perspective was that they would surely rather be out having fun, and they probably would be if the wife would allow it.
What I didn't realize, till I crossed that bridge myself, is that it isn't really about "being allowed". Once I had a family at home, my priorities changed. A night out was fun, but I liked being home to tuck the kids into bed. I really enjoyed spending time with my family, and any chance to get a good night's sleep was absolutely seized upon because it made the next day with the kids smoother.
Also, my financial priorities changed. I wasn't just thinking about myself anymore. A night on the town was always weighed against next week's grocery bill or next month's birthday party, or the need to have a little saved away for the next emergency.
Anyway...
There isn't really a good, succinct, way to explain all of that to someone who hasn't experienced it.
What you can do on the other hand is make it clear that you're not staying home with the family because you "have to" it's because you honestly want to.
Sorry guys, I've planned on spending time with my family. Dinner, hide and seek, bath time, story time, and tucking everyone into bed.
Rather than:
I can't, I've got kids at home.
These two statements send very different messages to your friends.
Side note...
Do make sure that you're taking some occasional adult time. It's good for you.
