I'm not exactly sure what context your professor brought this up in, so how I am relating them may not be what your looking for. I will start from the top level and work down.
Chromosomes are the structure seen within the nucleus of a cell that contain DNA and proteins. The proteins found in chromosomes are used to package DNA and control its functions.
DNA, also known as deoxyribonucleic acid is a molecule that contains the genetic material for all living organisms and many viruses. DNA is packed into a shape called a double helix and as we know, is organized into chromosomes.
DNA can be broken into sections called genes. There is a very large number of genes per piece of DNA and each gene will be a different segment of the DNA, containing hundreds of bases. Genes hold the information which allows a living organism to build new cells and pass genetic traits on to the next generation.
Each section of DNA is known as a gene and can have many variations. The variations or different forms of the same gene, are called alleles. Each allele of a gene will produce different traits because different proteins are activated with each allele. These slightly different proteins are what causes variation in observable traits.
Observable traits come from a gene and we all have different observable traits because of alleles. For example, a gene for hair color can have many different alleles and each allele will be related to a hair color.