To have a better understanding of the Brahma Sutras, we have to know a word - Laksana and its significance. The literal meaning of Laksana is the identifying features or attributes or very close to an metaphor. For example, while explaining the address of someone named Ram, we say, Ram's house is in the Ganga. We all know that Ganga being a river cannot be a place where someone could build a house. It means that Ram's house is in the banks of the river Ganga. This is known as the Tatastha Laksana. Tatastha Laksana is that expression by which we express a certain character of an object which is distinct from its real nature. The definition of an object that helps temporarily to identify the object, but which is discarded later for a better definition is called incidental qualification or Tatastha Laksana;
So, in the second Ap.( aphorism) of the Br. Su. ( Janmadhayashya Yatah), we find the use of Tatastha Laksana where the origin, sustenance and dissolution has been referred or related to the world which has no relation what so ever with the eternal, changeless and birthless Brahman but the second Ap. indicates the nature or characteristic of Brahman.
There is another way of expressing an object. Its the direct expression. In the scriptures, we find the references about Brahman such as -" Truth, Knowledge, Infinite is Brahman." This way of directly defining an object, here in case, Brahman is known as Swarupa Laksana. Through Swarupa Laksana, we define an object in its true essence. Here, though these three words are distinctive to each other and carry separate meaning when referred to in a different context, yet they talk about the one indivisible Brahman. For example, we say, H2O, two atoms of hydrogen and one atom of oxygen. H2O means water. Though 'H', '2' and 'o' are distinct, yet, they express the nature of one water. Another example is, Ram is a good father, a good son, a good husband and a good king. Father, son, husband and king are different, but they all refer to the characteristics of one person- Ram.
Why is the use of Laksana so important in Vedanta? It is because to understand and realize the depth of any given object and its definition, we should understand and realize at length the basic or intrinsic qualifications of those that construct that said object. In the Br. Su, we will find the references and need to understand the applications of such Laksanas often.