In directional (a.k.a. adaptive) selection, one extreme of a population has a selective advantage i.e. is fitter than other individuals of the population. This causes a directional shift towards this extreme in the population. An example of directional selection is in the evolution of antibiotic resistance in bacterial strains- for example in MRSA in which resistance to antibiotics is highly advantageous, so the allele for resistance is passed on to future generations preferably, and a large proportion of future populations are resistant.
Stabilising selection occurs when any change from a relatively intermediate value results in a decrease in fitness. This causes the phenotypic state to be stable across generations. An example is in body weight of babies- too small or too big leads to a lower chance of surviving.