Bringing up topic-based authoring immediately brings up the question of what, precisely, is a topic?
There are a bunch of answers to this question; I'm going to give you mine.
Very Short Answer
My first, very short, answer is that a topic is the unit of information delivery you write in when you move away from document delivery to information delivery as your organizational goal. While this answer is true, almost no-one finds it obviously helpful. It's the pure "what" answer with no obvious connection to how you would do such a thing.
A Heuristic for Information
The second, rather longer, answer starts with the formal definition of information.
That formal definition says information reduces the probability of uncertainty. The problem with this definition is that it's almost impossible to apply; you start having to think about ways to measure the probability of uncertainty in your customers, some of whom you may never know anything about whatsoever, in the future, before and after they've used your information delivery to try to do something unspecified. Thinking about the future accurately is very difficult; thinking about probability clearly is very difficult. The combination is nigh-impossible.
So instead of using the formal definition, fall back on a useful heuristic for determining what is information—information causes change.
This remains difficult, because information remains inherently contextual in terms of your audience. Instructions to an experienced mechanic about changing a tire need to contain little other than a torque specification for tightening the nuts and a list of relevant safety standards, where instructions to a complete novice need to start with how to identify the appropriate wrench. So human judgement about the intended audience has to be used to determine what constitutes information—what will cause a member of the intended audience to do something differently than they otherwise would have done—but "what would a member of specific audience do differently if they knew?" is a much easier question than "will this reduce the probability of an unknown individual's future uncertainty?"
DITA Topic As Audience-Specific Unit of Information
So, from this information perspective, a topic is enough information to cause one change, and enough context to understand that information.
Which information, and how much context, remain completely dependent on the intended audience. Relating information to audience is where the exercise of judgement by a writer first comes in to the topic-based authoring process; who am I addressing, what do they already know, what do they need to know to correctly decide what they should do? (Do, in a great many senses; deciding the answer to a question, deciding how to proceed with a job, deciding between alternatives...)
It's one change because topics are independent of each other, which includes their ordering with respect to each other. Once you have enough information to cause multiple changes in a single topic, you start to develop natural language dependencies in the content and lose the topic property of independence. The right way to handle "you have to know this other thing before you try to do this thing" is with explicit references, and DITA provides several mechanisms for doing making explicit topic-to-topic references.
Topics and Information Delivery
Using this definition, a topic is your unit of information delivery; it's enough information to cause one change in a member of your expected audience, plus enough context to understand that information. Because topics are organized in arbitrary groups, they require independence from one another, so all information dependencies should be expressed through explicit references to other topics, rather than through document order.
If you use topics in this way, there are a bunch of advantages; the most immediate advantage to a writer is that everything is in small pieces, relatively easy to keep track of and to have reviewed.Topics to this standard are also much easier to write, because the context is inherently limited; the context of organizations of topics making up an entire information delivery can be very large, and very complicated, but the context of an individual topic will be small and—by definition!—as simple as possible. This is a a big help to a writer.