Ok, I think this is a great question, and it is a problem that everyone in sci-fi or fantasy has to deal with to some extent. If you are in the far future or distant anywhere, you have that much more to explain. So don't.
Seriously. Look, you don't have to explain everything in great detail. Maybe there was a 'Great War' recently. Have a character mention his or her 'time in the Big One'. You don't have to go into details, but if you want to later, you can. The reader now knows that these people have somewhat recently dealt with a large-scale war, and all that entails.
Maybe you have some new technologies, say an Alcubierre-based gravity warping drive. Do you need to explain that in 2340 they were able to tap into quantum energy, which allowed both power and an alternate method for creating the gravity warping than dark matter? Nope. Explain that so-and-so drive was developed in <insert year>, warps space, and allows FTL speeds within relativity by moving the frame of reference. Minimal details. Tell what it does.
From a social standpoint, have them think whatever they think, based on their situation. Sometimes it is better to leave the question mark there. If Joe talks about something that seems unusual to us today, and the other characters appear to take it in stride, the reader will generally go "I wonder what that is all about" and give you space. You can then use a reflective scene to bring out more of the history.
On a side note, think about the movie 300. Those events occurred in 480B.C. A thousand years from now, do you think there will be entertainment centered around key battles from our time's world wars, for instance? You betcha. Use that sort of thing to draw compairsons. Just a thought.
That's just my thought.