A DNA sequence is just that: it is a specific sequence of all those little bases, the whole distance along the DNA strand from one end to the other. Let's talk size and amount, for a moment:
DNA in different organisms is constructed of different numbers of nucleotides, so each DNA strand will be a different length and complexity according to which organism it is for. Humans are very complex organisms and a single one of our DNA strands contains a few BILLION nucleotides, while simpler life forms will have DNA strands with fewer, into the millions or less. The more body parts you have, and the more intricate their functions have to be, and the more details they have, the more 'information' your DNA sequence needs to hold, since more complex blueprints are needed for more complex structures, right?
We have so many nucleotides, a single strand of human DNA stretches to about seven feet, if laid out straight! Yet it is so thin that even 'bunched up', curled up around itself, you can't even see it as a tiny dot, without a powerful microscope. Let's blow that up into a larger picture: if that DNA strand were enlarged to around two inches wide, like a two-inch-wide ladder... it would stretch all the way around the equator of the earth! Now, that's a lot of information packed into a tiny, almost invisible strand!
Each of those rung-like bases tells your body's cells what to do, where to go, what kind of a cell to become. Your entire DNA sequence will tell a cell to become part of a hair or a skin pigment or a fingernail. Not only that, it will tell that cell to grow a particular way - it will tell that cell to grow a little bit like the cells in each of your parents grew, but in a slightly different mix that has similarities to each parent and yet is also different than both. That is why your face will look a little like your Mom and a little like your Dad; your entire DNA sequence has some segments, some shorter 'stretches' of sequence, that are the same as or very similar to each parent, and yet all your sequences are put together in a slightly different order so you will still look different than both parents; you'll look unique. And that's what we call YOU.
Back to the DNA sequence: if you were to paint each of those bases a different color, like 10 blue rungs and 10 red rungs, you could sequence them in many ways: all 10 of blue and then all 10 of red and then 10 blue again and so on; or in alternates of 5 and 5 of each; or in alternates of 2 of each, and so on. And you could also arrange them in non-even order, like 1 blue, and then 2 red, and then 5 blue, and then 8 red, and then 2 blue, 1 red, 4 blue, so they seem very random. With billions of nucleotides along the length, a DNA strand can have millions of combinations of those nucleotides, each one a little different sequence than anyone else's.
That is what a DNA sequence is, simplified. It is the order that those DNA bases are arranged in along those seven or so feet of your DNA strand. Instead of colored rungs, remember that each base is either Adenine-Thymine or Quanine-Cytosine. But it's easier to say blue or red. DNA sequences are not random, and we are trying to find out which sequences correlate to different parts and processes of the body. Again, using that 2-inch-wide ladder stretching around the Earth... maybe the sequence for your left leg and all its parts, bones, veins, skin, hair, muscle, nerves, is 5,000 miles long? Maybe the DNA sequence for your hair color is only 300 miles long? Maybe the sequence for your eye color is 200 miles long? That's what DNA sequencing is all about: mapping those sequences of DNA and identifying their patterns. Read on.