Table accessibility is divided into two areas - tables used to present data and tables used for layout purposes.
The basics of data table accessibility is to make sure you have properly labelled any row or column headers. If the table has a simple layout, meaning only a single row and/or column of headers, this technique is fairly straight forward and easy. If your table layout is more complex, such as using merged cells or having multiple rows and/or columns of headers, there are a few extra steps you need to take to explicitly associate each data cell with its corresponding header cell.
While layout tables are not nearly as popular since the rise of CSS, they are still used sometimes. In fact, WCAG 2 still allows the use of tables for layout, but encourages authors to consider using CSS instead.