Answer:
This phrase means that nonalignment allowed underdeveloped nations to receive financial assistance from foreign nations without the imposition of conditions.
Step-by-step explanation:
To "attach strings" to a particular thing is an idiom that means "giving on a condition". The phrase from the passage is saying that nonalignment has several benefits, one of which is that impoverished and underdeveloped countries suffering the aftermath of World War II can benefit and receive assistance from developed nations without these developed nations subjecting them to some conditions.
An example is given in the passage of the United States refusing to help Egypt in building the Aswan Dam because they sought Communist help. The strings attached to the help by the United States is dissociation from communist nations. Nonalignment enabled Egypt to get the help they needed from the Soviet Union.