When you run an agarose gel for DNA sample, you should get a tight band of high molecular weight.
There could be many reasons to get a smeared faint band of DNA.
1. The smeared band indicates degradation of DNA. It could happen during the extraction process. You should avoid nuclease contamination. Make use of DNase inhibitors while extracting genomic DNA.
2. The appearance of smeared band could also be due to improper electrophoresis conditions. Do not allow voltage to exceed ~20 V/cm and maintain a temperature
it looks like degradation.... du to nucleases during the extraction or your sample has not been kept frozen... it can also be du to shearing during preparation; do not vortex your sample, avoid repeated pipeting...
there is always a little smear with long genomic DNA but you should get a clear band >20kd (over the higest band of the lambda MW)
I concur with the other answers that you are most likely seeing genomic DNA. Are you trying to purify genomic DNA or plasmid DNA? If this is supposed to be plasmid then you are probably being too harsh during the lysis step such that genomic DNA is being released. If it is supposed to be genomic DNA then as Didier Poncet states you are probably shearing it due to excessive vortexing or pipetting.