The low pressure system wind flow in a counterclockwise direction toward the center because low pressure are connected, and in fact often generally, by upper atmosphere with winds. Winds generally blow from high pressure to low pressure areas at the surface. The direction of deflection is caused by the rotation of the Earth and the resulting Coriolis effect.
A way to remember this is.....some stoners like to get "high around the clock" (as in clockwise, but please don't do this!!)
Low pressure systems usually bring cloudy stormy conditions, while high pressure system bring clear bright skies and in the summer, warm weather.