At high pH, basic compounds will be deprotonated, making them less polar/more hydrophobic. As such, the basic compound will be better able to interact with a hydrophobic stationary phase such as that provided in a C18 column. This results in longer retention times.
An additional benefit is secondary interactions are reduced, improving peak shape.
Finally, increased retention of basic compounds typically leads to elution in higher organic, which may help ionization in LC/MS applications.
Basic compounds therefore retain longer, with better peak shape, when you work at high pH.