One way of describing it is to say that Jesus shifts our perspective from apocalyptic to eschatology. (Eschatology is simply the study of the last things; the 'eschaton' is the end, the full stop at the end of time). Christians are called to live in the light of the end of the world, in the light of the last judgement.
Now when Jesus is talking about this, he uses images that are sudden. They will come like a thief in the night. Or think about the parable of the wise and foolish virgins, or the story about looking after your house, he emphasises suddenness, the immediate nature of it and so we are called to live as if it is about to happen. There is a phrase which Christian theology uses to talk about this perspective and its called a realised eschatology. What that means is that the end of the world in breaking in an applicable way now, and so we live in the light of it now. It is not something that is happening in the future to which we need not pay any attention.
Think of a bus driving along a mountain pass, and imagine that the driver has absolute certainty and conviction that he will get to his destination safely, that if for example he should go off the edge of the mountain, there are these wonderful angels who will lift the bus back on to the road. That bus driver will view things rather differently than the bus driver who does not have that certainty but expects something dangerous to be possible and therefore pays attention to that present moment and lives consciously and attentively to ensure that he drives properly and does not go off the edge of the cliff. Apocalyptic is the perspective of the first bus driver who has got a certainty about where things are going and therefore does not worry too much about what happens in the meantime. That is the 'left behind' understanding; that is the understanding that says, “Yes let's have a war between Israel and the Arabs because that will bring about the Second Coming.” Realised eschatology, in contrast, is the second bus driver. This is the perspective that Jesus is teaching, saying that we have to concentrate and live in the light of the end of the world now. We actually have to pay very close attention to each moment in time because the judgement could be just around the corner. The normal Christian way of describing this is to talk about 'living in the Kingdom'. A great deal of standard Christian language and doctrine has its roots in this perspective. It is the vision which structures Christian ways of thought, which was inaugurated on Easter morning, and which shapes and conditions the way that we live here and now.