How to use connections between tables?

Those columns are used to link together the tables and their entities. Giving you a specific scenario, just think of the following content,

Account
id | name | ...
1  | ABCD | ...
2  | EFGH | ...

Sessions
id | account_id | ...
1  | 1          | ...
2  | 43         | ...
3  | 3          | ...
4  | 1          | ...
5  | 2          | ...

For example, in the states where you want to show all the sessions linked to a specific account from both the tables, you would use the ID from Account and Account_Id from Sessions table to "JOIN" them together. In SQL JOIN, you specify which records to JOIN based on which criteria — the columns.

Thus, getting something like this,

Account.id | Sessions.id | name | ...
1          | 1           | ABCD | ...
1          | 4           | ABCD | ...

Then further stuff is your own logic to use the data, how? That is all upto you, basically this is done on the tables that have been normalized. You remove a few common anomalies from the tables, and you remove some data redundancies. That step results in more than 1, 2 or even 3 tables sometimes. Thus getting the data back requires you to JOIN the tables. These columns — account.id, sessions.account_id — act as the pivot points for your tables to be JOINed at.

For a better explanation of how to JOIN the tables in SQL, please read the following articles,
Visual Representation of SQL Joins[^]
Types of Join in SQL Server[^]
Database normalization - Wikipedia[^]