As we know from the news and, all too often, from our own personal experiences in the fall and winter flu season, the effect of flu viruses that mutate is that they are able to overcome the body's existing immune defences. This is both the nature and the purpose of all viral mutations: the body's immune system is geared to defending the body from threats it has already encountered, and when it encounters a new, mutated virus, it may need time to produce new antibodies before it can effectively fight the new threat. Many of the most common as well as the most dangerous viruses in the world have evolved in ways that allow them to mutate quickly, so that they can infect the same population (and, indeed, the same people) over and over again.
Under normal circumstances, the body's immune system is highly effective at detecting and then eliminating foreign bodies which it has previously identified as threats. White blood cells in the body's immune system mark virus particles and other identified foreign bodies, and other such specialized cells then absorb and destroy them. Once sufficient exposure has occurred for the antibodies to be manufactured, in most cases the virus can be safely destroyed on any subsequent occasion when the body encounters it. There are some exceptions to this, because a few viruses have evolved special ways to trick, sidestep, or even infect the immune system, such as HIV. In general, however, once you have had a particular flu virus, you cannot get it again. The same philosophy lies behind our feeling of security from "childhood" diseases such as chickenpox: once a child has got chickenpox, she or he generally cannot get it again, unless their immune system is compromised.
Viruses, however, have developed ways of getting around this defences. One of the most common is simply to mutate, altering their genetic code and changing their appearance or makeup enough that the immune system no longer recognizes it and has to go through the whole process of identifying it as a foreign body and producing antibodies again. Some viruses are particularly prone to mutation, so that by the time a person is exposed to the virus a second time, it may well have changed enough that they will become infected and suffer illness all over again.
The common cold is one of the most adept at this process, which is why there is no vaccine or effective treatment for the cold. Influenza is also heavily prone to mutation, because it lacks the protective mechanisms in its RNA which normally safeguard against mutations. This, combined with the scale of viral populations (one host could easily be infected with millions of copies of a virus), makes mutations relatively common, and also makes them able to spread very quickly. For this reason, the dominant flu in one flu season will normally be mostly unrelated to the dominant flu of the previous season - which is why, each year, we seem to lack immunity to the new strains.
Fortunately, the flu mutations are usually predictable enough that pharmaceutical companies can make an educated guess about the likely major flu outbreaks some time in advance, and build these into their annual flu vaccines. However, occasionally they miss a mutation - and this is particularly the case when flu viruses jump into humans from their other natural populations, pigs (swine flu) and birds (avian flu).
The precise effects of a given mutation are essentially random: some mutations generate more virulent and more dangerous flu viruses, while others generate less potent ones. In all cases, however, major new mutations will result in more harmful effects for the very reason explained above: the body lacks a defence prepared in advance, and therefore will not be able to fight off the virus quickly enough to prevent the body from suffering the illness we know as the flu. Fortunately, in almost all cases, those who have contracted a new, mutated flu virus will still be able to manufacture the appropriate antibodies relatively quickly, so that the disease goes away in several days' time.
Because the extent of the changes caused by mutation and viral recombination can result in greater or lesser ability to overcome the body's existing immune defences, those which are most significantly altered are usually those which most easily spread through the population. It is for this reason that public health officials are particularly concerned about new strains of swine flu or avian flu jumping to humans: these viruses have lived in other species for some time, so that if and when they jump, we are exposed to a large number of new mutations against which we have no defences.
Again, however, the danger from such viruses will depend on more than simply the body's lack of immunity. Last year's swine flu pandemic, although it spread quickly and was quite frightening, was moderately more lethal than the average annual flu outbreak. However, occasionally much more dangerous flu pandemics can occur. The Spanish flu of 1918-1919 killed over twenty million people, more than the First World War which immediately preceded it.