DNS propagation is the time delay between the time you make DNS changes on your authoritative DNS servers, usually at your hosting provider, and the time it takes for these changes to be seen by your end-users and customers.
The time it takes to propagate is going to be based on your current time to live (TTL) settings for the resource record you changing.
These TTL values must expire from the recursive DNS servers around the Internet. Meaning the recursive DNS servers at ISP around the world.
Once the TTL value reaches zero the recursive DNS server will then need to ask the authoritative DNS server for the new answer.
The higher the TTL value the longer it takes changes to propagate because it will take longer for the cached value to expire.
These tools will query several recursive DNS servers at random ISP's around the world to report on what IP address they are currently returning to their end users DNS queries for your domain.
This will help you gauge if the changes you have made are being propagated on time.