Nothing really. However, it is conventional to present an x axis horizontally and y axis vertically.
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The y intercept is the point along the y axis at which the line (or curve) intersects. So, if your the line graphed from your equation crosses the y axis at y=1, then 1 is the y intercept. x will always be equal to zero at the y intercept, so if you plug 0 in for x and solve the equation, you get the quantity of the y intercept.
The x-axis comes first. because x comes before y.
The x-axis is the horizontal axis on a graph. The y-axis is the vertical axis on a graph.
In a Cartesian grid, the x-axis is the horizontal axis, and the y-axis is the vertical axis.
In notation of coordinates it is the x axis followed by the y axis