For Row:
mainAxisAlignment = Horizontal Axis
crossAxisAlignment = Vertical Axis
For Column:
mainAxisAlignment = Vertical Axis
crossAxisAlignment = Horizontal Axis
These two pictures are clear to show the meaning of MainAxisAlignment and CrossAxisAlignment.
When you use a Row, its children are laid out in a row, which is horizontally. So a Row's main axis is horizontal. Using mainAxisAlignment in a Row lets you align the row's children horizontally (e.g. left, right). The cross axis to a Row's main axis is vertical. So using crossAxisAlignment in a Row lets you define, how its children are aligned vertically.
In a Column, it's the opposite. The children of a column are laid out vertically, from top to bottom (per default). So its main axis is vertical. This means, using mainAxisAlignment in a Column aligns its children vertically (e.g. top, bottom) and crossAxisAlignment defines how the children are aligned horizontally in that Column.
Row/Column are associated to an axis:
Horizontal for Row
Vertical for Column
mainAxisAlignment is how items are aligned on that axis.
crossAxisAlignment is how items are aligned on the other axis.
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