This would apply to the x-axis, assuming your histogram has vertical bars. Bin size is not the space, but the size of the interval.
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A bar graph consists of measurements depicted as bars. Each bar represents a 'bin' with a value that determines the height of the bar. The interval is simply the increment from one bar to its nearest neighboring bar.
Let's say the following bar graph is the number of apples of a certain size. 1", 2", 3", 4" etc. The interval is one inch. And obviously in this graph, there's a lot of small apples and very few big ones.