Where would you be without cell death, well dead I reckon. Cell death is needed in development to shape you body, such as give you fingers by killing the webbing between them. Not only that, but cell death is needed to shape the development of the brain. These things are done by apoptosis, what I would describe and the clean way of dealing with dead cells. They get broken down by nice signals outside the cell or if something internal goes wrong they order themselves to die (like by p53 to stop the cell becoming a cancerous cell and killing you). When they break down they do it in such an ordered way you wouldn’t really notice it, the dead parts get eaten up by near by cells and no nasty lysomal enzymes get released to damage the rest of the tissue. However not all cells die in this lovely way. Necrosis is where the cell is damaged and really just bursts open and releases lysomal enzymes that damage the tissue and it causes an inflammatory response by releasing HMGB1 from the nucleus into the extracellular environment to clear away the corpses of the cells.
However the two may not be so distinct. The same injury can cause either and if the apoptosis mediators are not functioning through mutations then necrosis can take over. If ATP levels drop in a cell going through apoptosis necrosis kindly steps in and does the job. Necrosis seems to have a controlled cellular pathway involving ROS, calcium signalling and proteases being activated. Some of the necrosis program appears to work in the background of apoptosis and parts of apoptosis keep the death ordered. Necrosis also (sometimes) is beneficial to an organism. In rabbits it has been reported that excess cells in theur growth plates down by necrosis.
So necrosis may be damaging and causes a lot of brain damage in strokes and Alzheimer's disease, but it is probably a backup program for when apoptosis fails to handle the situation rather than simply the cell bursting open!The figure is from: Leist M. and Jäättelä M. (2001) Four deaths and a funeral: From caspases to alternative mechanisms. Nature Reviews Molecular Cell Biology 2: 1-10.