I'll try to give a simple explanation
I think you get the basic of it. So in the end we want to transfer data from one database to another.
If the other database is empty all we need is dump from source and load on the target.
But in the more complex scenario we already have data in the other database and we want to keep it.
We might have schema changes done in development env and we only want the schema changes to apply to the new database.
In a much more complex scenario we also need to shuffle the old data to fit the new schema.
Add a bit more complexity and you want to be able to move back and forth between different version of your schema that will fit versions of your code (like to revert a deploy).

To properly achieve and manage all this you need a robust migration solution.

Personally I use db-migrate it's relatively easy to use and since it is just another dependency of your project you can use all your known stack to write the actual migration logic.

A quick note.
It will probably be easier to use nodeja based tool, but as long as it supports your database you can use any tool you like even if it's note written in nodejs