The Borel Sigma-Algebra is a collection of sets that arises from the concept of open sets in a topological space, particularly in the context of real numbers. It is generated by taking all open intervals and applying operations like countable unions, countable intersections, and complements. This structure allows for the formal treatment of measurable sets in analysis and probability. In practical terms, the Borel Sigma-Algebra includes not only open sets but also closed sets, countable sets, and more complex sets formed from these. It plays a crucial role in defining Borel measures, which are used to assign sizes or probabilities to these sets, facilitating rigorous mathematical analysis.