There are two main reasons for the strength of Prussian military at two different periods in history.

In the early period, around the time of Frederick the Great but more importantly his father who prepared the groundwork for Frederick's successes it would be introducing country-wide conscription. Prussia ended serfdom but at the same time it ensured that everyone was liable for service to the country. It also established a system in which military service was a secure and viable route of social and economic advancement. It was the same solution which later would give France the edge over its opponents by being able to utilize huge reserves of manpower. You have to realize that Prussia at the time faced feudal countries which relied on volunteer or impressed forces and which kept huge populations working in agriculture as serfs, without rights of citizens. The motivation which Prussian reforms gave the former serfs was crucial in allowing them to field large armies despite being much smaller than their opponents.

In the later period it would be the creation and development of the general staff which was a system of education for officers which standardized and accumulated military planning. It also established a professional cadre of planners which then would be assigned to commanders who while sourced traditionally from nobility had the benefit of being trained in staff colleges themselves and at the same time being taught to consult with their staff as means of improving the efficiency of the army as a whole. This ended the practice of treating military careers as entitlement and command as personal whim of the nobility.