"Strategy" refers to a plan to reach a goal. When one is preparing to undertake a task, the plan to get the job done could be called the strategy for accomplishing the task. "Strategic importance" is a way of evaluating how important a particular part of the plan is in the overall scheme of the work.
In historic terms, the "strategic importance of a place" refers to the key impact location has played in deciding how important certain places have been during events. Boston and Philadelphia and New York City became critically important locations during the colonial years and continued to be so during the American Revolution because of the "strategic importance" of their locations. All three cities were located in large natural harbor areas that made them easily accessible to shipping of supplies from overseas. All three also were also located at the mouths of rivers that simplified transportation of goods and people from inland to the population centers on the coast.
There are numerous other examples of places that became known to history because of their strategically important locations.
If a place is of "strategic importance", it usually means it is vital to the military and economic wellness of a country. These places become targets during times of warfare. In times of peace, efforts are made to improve the infrastructure of these locations.
There are a number of factors that make a place "of strategic importance." The geographic location of a place is important. Places located near major lines of transportation are usually vital. In the past, that would have meant coasts or rivers, but today can mean highway, rail, or air routes.
Larger populated areas have value because of the human resources available. Manufacturing centers are also considered strategically important, especially in times of warfare. A place could be of strategic importance if there is a wealth of resources in the area, particularly resources that can be used for manufacturing.
A place can be strategically important for various reasons. It could be important from a military perspective. For example, a place with higher elevation will provide you with a good vantage point; a narrow valley will force the enemy forces to divide and move through in small numbers, etc.
Similarly, a place can be strategically important from a manufacturing point of view. A strategic location may have one or more of these advantages: availability of cheap labor, raw material, easy and accessible transport, resources including water and electricity, etc. An example is the East Coast corridor from Worcester, MA to Providence, Rhode Island; a 45-km stretch that served as the birthplace of the industrial revolution in the US.
A place can also be strategically important because of its historic significance and heritage. An example is Philadelphia.
Thus, strategic importance simply refers to some attributes that make a place significant.