An outcome measure is used to measure the success of a system. For example, the outcome measure could be the percentage of people who do not get polio (the result). An output measure, for example, would be the number of people vaccinated with the polio vaccine (the output). Often we measure inputs (amount of money spent) or outputs (number of people vaccinated). They are usually easy to measure but obviously less valuable proxies for what the objective of the system (reducing the incidence of polio).
You should have all these types of measures but outcome measures are most likely to be missing so special care should be taken to make sure you are using them. It is important to define good outcome measures to use in determining the success of systems, and in determining the whether improvement projects actually result in improved outcomes.
In-process measures can be valuable in providing actionable information sooner than the outcome measure would allow action. In the polio example, an in process measure example could be % of vaccination by the time a babies is 18 months old. And looking across a country say it might well make sense to stratify the data to see if certain areas were doing poorly on this measure. If so that might be where to focus improvement. You don’t need to wait until people not vaccinated start contracting polio (which will likely be delayed for years after the system starts to have processes fail, in this example) to then notice the problem and then react.
Waiting for the outcome measure to point to a problem in this case (and in many cases) is far too late for process improvement. So process measures are needed to aid in managing the system and reacting to process results, before those processes create poor results (and can be seen as poor outcome measures). More on outcome measures.