A dominant trait is the one which is exhibited as a phenotype even if the individual only has one copy of the dominant allele (also known as being heterozygous). For example, the allele for brown eyes is dominant, therefore you only need one copy of the brown eye allele to have brown eyes (although, with two copies one will still have brown eyes).

A recessive triat is the one which is phenotypically exhibited only if the individual has two copies of the allele (also known as being homozygous). For example, the allele for blue eyes is recessive, therefore to have blue eyes one needs to have two copies of the blue eye allele.