They are both methods for looking at sizes of particular polynucleotides. Southern blots are for DNA while Northern blots are for RNA. The methods are basically the same, though the electrophoretic conditions are slightly different. The method first involves running the nucleic acids out according to size on some kind of gel, be it agarose or polyacrylamide. The nucleic acids are then mechanically transferred (either by capillary action or by electroblotting) to a membrane like nitrocellulose or cellulase acetate or a polyamide of some kind, to which the nucleic acids are irreversibly trapped. The membrane is then probed with labeled oligonucleotides that hybridize to a nucleic acid sequence from the gene you are interested in studying. After hybridization, the membrane is "developed" to reveal the location of bands of nucleic acids that can hybridize to the probe. The location of the band on the gel tells you something about the size of the polynucleotide of interest. It used to be that "labeled" meant radioactively labeled, but nowdays there are chemical lables that work by chemiluminescence or fluorescence.
southern blotting is a procedure for detection of DNA. It is a highly reliable and accurate procedure to find out even very trace amount of DNA present in elcrophoretic gel meterial. In this technique a gel meterial(PAGE or Native) is blotted to a nylon or cellulose membrane, to which radioactively labelled antibodies are fixed.