Here's just one possibility. Say you want to do genetic testing for susceptibility to a particular trait, for example heart disease. The human genome is vast, and no human could pick out significant patterns relating to heart disease even with years of experience and specialist training.
However, this is precisely the task at which machine learning algorithms excel. You split your data into two sets: people who suffered heart disease by time X in their lives, and people who didn't. You then apply a machine learning technique (some kind of classifier - maybe a logistic regression, support vector machine or a decision tree) to the data set, and it picks out features (i.e. particular gene sequences) which are most strongly predictive of heart disease. If you've chosen the right technique, you can not only predict a binary yes/no response, but you can predict a probability between 0% and 100%.
Now you can do genetic testing on an individual who hasn't suffered heart disease yet - with a suitable portion of their genome, you feed it into your classifier and it spits out the probability of them developing heart disease by stage X in their life.
Of course, the inputs don't have to be genomes (and quite commonly aren't). You might consider someone's age, calorie intake, level of exercise, social class etc. all as valid inputs to this kind of algorithm.