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Outliers increase the standard deviation. Mean is most affected by outliers, since all values in a sample are given the same weight when calculating mean. A value that is far removed from the mean is going to likely skew your results and increase the standard deviation. Say you have five values: 2, 1, 2, 1.5, and 2.1. Your mean would be 1.72 and your standard deviation would be 0.47.
The graph of the normal distribution depends on two factors - the mean and the standard deviation. The mean of the distribution determines the location of the center of the graph, and the standard deviation determines the height of the graph. When the standard deviation is large, the curve is short and wide; when the standard deviation is small, the curve is tall and narrow.