It is considered that a shape, eg. Rectangle, with the golden ratio looks "most pleasing to the eye".
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The golden ratio is the ideal ratio because it is consistent throughout many aspects in nature - proportions of the human body, the crests and troughs of a heartbeat, the stripes on a tiger's head, et cetera. The value of the Golden Ratio is 0.5*[1 + sqrt(5)] = 1.61803 (to 5 dp)
The value of the Golden Ratio is (1 + sqrt(5))/2. It is visually appealing because it is!
There is no single ideal ratio.
The golden ratio (golden section) is the division of a line so that the whole is to the greater part as that part is to the smaller part (i.e., in a ratio of 1 to 1/2 (√5 + 1)), a proportion that is considered to be particularly pleasing to the eye.
There are both golden triangles and golden rectangles. In order to be considered golden the ratio must be the same as the sum of the longest side to the other two sides.