DNA is a (bio)chemical way of storing genetic (biological) information. It is basically a long stretched-out molecule consisting of modules (nucleotides, or as they're often called: bases). There are only four modules in a DNA molecule and they are the language in which the information is stored. The four nucleotides of which the DNA strand is composed are Adenine, Cytosine, Guanine and Thymine. The DNA molecule really consists of two strands of this long molecule, twisted into a helical shape. If on the one strand there is and Adenine (A) at a particular position, the other strand always has a Thymine (T) at that very same position, across from the A. The A and the T are chemically bonded to each other by 2 hydrogen bonds. In the same way Cytosine (C) and Guanine (G) always pair up using 3 hydrogen bonds. Because A always bonds with T, and C always with G, one only needs to know the sequence of the nucleotides on the one strand to know exactly what the sequence of nucleotides on the other strand will be. What I will refer to as a gene later on, is simply a stretch of DNA, with a start and an end.
The pretty picture of the DNA helix above is credited to brian0918 and was taken from http://en.wikipedia.org/wiki/Image:ADN_animation.gif
As cells divide, they need a duplicate of their genetic information, their DNA. To do this, the DNA helix is separated and a protein complex reads the information on the one strand, to produce the other strand (this is called the complementary strand). Since the same is done to both of the original strands, after DNA replication is complete, there are two copies of the original DNA molecule(s). After all the DNA in a cell is replicated, the cell can divide in two, which each half getting a complete set of DNA.
Transcription of DNA refers to production of a molecule called RNA, which is similar to DNA, but different in a few respects. Only one strand of RNA is made at the time, instead of 2 during DNA replication. RNA does not have any Thymine, but uses Uracil (U) instead. And lastly, each RNA nucleotide has a slightly different chemical make-up than a DNA nucleotide, it is made up of ribose sugars, instead of deoxyribose sugars like DNA.
Reverse transcription is the process by which an RNA molecule is read and converted into DNA. Retroviruses use this method to convert their genetic information, which is in the form of RNA into DNA. The DNA can then be inserted into the genome of the host. Handy tool, isn't it?
During the process called translation, a particular kind of RNA molecule (messenger RNA, mRNA) is read by a large protein complex called the ribosome. The ribosome "reads" the sequence of nucleotides, and stitches together strings of amino acids, one for every three nucleotides it has read. The amino acid strings are called peptides, or proteins and fold up into complex three-dimensional structures. These proteins are the big workers in the cells. They carry out all chemical reactions, including the processes described above of replication, transcription, and translation. Proteins are the workhorses of the cell.