I couldn't find anything on internet that would give a clear-cut idea about what it could be.
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Topology is the study of flexible geometries. That is, what properties do objects have when you're allowed to stretch and bend them (but not allow them to break or pass through themselves). This is the origin of the saying that to a topologist there's no difference between a doughnut and a coffee cup. Topologically, they're the same object. If the doughnut and coffee cup were made of really elastic putty, you could remold one into the other without cutting it, or allowing it to pass through itself.
So what does this have to do with DNA? Well, while DNA is stiff on short scales (dozens of base pairs), when you get long stretches of DNA it's very flexible. You can bend and wrap the DNA up. But there's a limit on what you can do without breaking it or letting it pass through itself. (For circular DNA) You can't get knots, and the intrinsic double-helical "twist" of the DNA can't be changed.
There are various enzymes in the cells (helicases, topoisomerases) which are responsible for controlling this coiling and twisting. The way they work is to (temporarily) make a break in the DNA, pass the DNA strands through the cut, and then reclose the strands. That is, they change the topology of the DNA. This is how you get "overwinding", "underwinding" and "supercoiling"
So "the topology of DNA" is talking about the properties and geometry of DNA that it has if you treat it as an unbroken floppy noodle: how it's wrapped up and how it's twisted.