I know that a SQL dump is a series of insert SQL statements which reflect all the records inside the database. But what is it used for? Why should we dump the database records?
mysqldump produces an SQL representation of the data for one or more tables or databases. As the format is SQL, it will run on any other MySQL server, regardless of architecture or major/minor version (obviously, views won't work on 4.x etc. but it is mostly forwards compatible).
There is another tool, mysqlhotcopy, but as this tool produces binary files, they are tied to the machine they have been generated on, and cannot be used elsewhere. SQL has the advantage of running on any MySQL server, and being independent of the underlying file storage mechanism of the database(s).
The two main use cases for dumping SQL are:
There are some less common uses. For example, SQL snapshot of your application's database could be taken for unit testing against a known state. It is also possible to transform SQL code into another dialect, e.g. PostgeSQL or SQLite, to port your data to another database.
You asked if other databases provide SQL dump functionality. The answer is yes in almost all cases. PostgreSQL provides pg_dump, SQLite has a .dump
command, etc.