One standard way to construct both a Möbius strip and a Klein bottle (and other classic manifolds) is to take a square, and glue some edges together.
For a Möbius strip, you glue together the left and right (say) edges, such that the upper part of one connects to the bottom part of the other (that is, put a twist in the square before you glue).
For a Klein bottle, you additionally glue together the top and bottom edges, but don't twist them. This is what it means to say a Klein bottle is "like a Möbius strip" or "two strips glued together" or similar things.
The "4d" comes in because if you want to do this with a physical object, you need four spatial dimensions unless you're ok with it passing thru itself.
One standard way to construct both a Möbius strip and a Klein bottle (and other classic manifolds) is to take a square, and glue some edges together.
For a Möbius strip, you glue together the left and right (say) edges, such that the upper part of one connects to the bottom part of the other (that is, put a twist in the square before you glue).
For a Klein bottle, you additionally glue together the top and bottom edges, but don't twist them. This is what it means to say a Klein bottle is "like a Möbius strip" or "two strips glued together" or similar things.
The "4d" comes in because if you want to do this with a physical object, you need four spatial dimensions unless you're ok with it passing thru itself.
Here's a good picture : http://web.ornl.gov/sci/ortep/topology/topo5.gif The arrows indicate which edges to glue together, and how to line them up.
See also bmm6o's comment here: https://news.ycombinator.com/item?id=11196493