In a Molecular Biology lab i did several weeks ago we did a Transfection in which we CaCl treated and heat shocked E. coli to take up naked DNA plasmids. So basically, Transfection means to take up DNA.
A more accurate definition from my trust old One Look dictionary search thingy gives me: The uptake, incorporation, and expression of recombinant DNA by eukaryotic cells
The introduction of DNA into a cell or organism using recombinant DNA technology.
The process by which exogenous DNA in solution is introduced into cells. The introduction of foreign DNA into eukaryotic or prokaryotic cells.
As for transformation, from Microbiology by Prescott et al:
Transformation: A mode of gene transfer in bacteria in which a piece of free DNA is taken up by a bacterial cell and integrated into the recipient genome.
The uptake in culture by recipient cells of foreign DNA. The cells are either treated with calcium phosphate or subjected to an electric field (electroporation) to make their membranes more permeable. A standard procedure for introducing foreign DNA into mammalian cells.
A genetic alteration to a cell as a result of the incorporation of DNA from a genetically diferent cell or virus; can also refer to the introduction of DNA into bacterial cells for genetic manipulation.
From my molecular bio notes:
Transfection is the use of viruses to transfert foreign DNA into a cell whereas transformation is the various methods of transfert of foreign DNA into cell (Chemical/heat-shock, electroporation, natural)