A row describes a manner in which objects can be organized. Rows are commonly used with columns to form an array, though this doesn't have to be the case; both rows and columns can exist as single rows or columns. Most typically, rows are thought of as being horizontal, while columns are thought of as being vertical. This however, is mainly a convention, since depending on perspective, you could rotate something such that what were once rows, become columns based on their definitions of being horizontal or vertical.
In areas such as a stadium, movie theater, gymnasium, or anywhere where organized seating can be beneficial, the seats are often set up in rows. It is common to have rows that are labeled in terms of numbers and letters. For example, you may have a seat labeled "A4" which could refer to row A, seat 4. It's also possible to have a seat "4A" that could mean row 4, seat A. These are not the only way to label rows, but they are fairly commonly used methods.
Below is an example of stadium seating where you see can that the chairs in each row are the same color, while those in other rows may be a different color than the row adjacent to it. In this particular stadium, the rows are indicated both by color as well as seat number.
It is also common to see rows of crops, trees, or plants. You may see trees alongside the road that are planted in rows, or crops on a farm planted in rows. You may even have plants in your own backyard organized in rows. Part of the reason for this is that rows can be a rather convenient way to arrange things in a simple, orderly manner.
Though matrices and vectors are outside the scope of primary math, they are examples of two other ways that rows are used in mathematical contexts.