What would be your ideal first lecture in a databases course?
Similarities

For a first lesson, what you want to focus on are anchor points, i.e. how databases are something that's closely related to what students already know and understand.

The prime example here is Excel. We've all seen a data table at some point, e.g. your grades/report card from school are a data table, or your bank transaction history.
My SO is currently in the process of a career change in IT, and I suggested her to substitute "table" with "Excel file", and it really helps to understand the big (though certainly massively oversimplified) picture.

Understanding that, a database can easily be described as a folder of Excel files. This is again massively oversimplified, but enough for an introductory understanding of what a database's purpose is.

Note that you could also represent a database as a single Excel file with multiple sheets. However, for display purposes I prefer having my tables in separate windows, which is easier when working with separate Excel files. It's purely a visual decision.



A practical example

My favorite example, probably because it's what I was taught as a first example, is Blockbuster, i.e. a simple video renting service. It's an example that can be adapted to students' growing understanding of a database structure.

In a first version, you have a single table where each record represents a rental, with customer info (e.g. name), DVD info (e.g. movie title), and rental info (e.g. return date)

If a customer rents multiple videos at the same time, it quickly becomes cumbersome to have to repeat their personal information, which leads to version 2: separating the customer information into its own table, and referencing the specific customer (by ID) in the rentals table.

The same logic then also leads you to separating the video tapes into a table of their own, analogous to the customer example.

This three table structure is fairly straightforward, easy to develop from what was initially a single table, and it teaches most core concepts for database modeling: tables, columns, records, primary keys, foreign keys, and the basics of data normalization.



Database design is a theory, not a technology

It's interesting to note that you could, time permitting, demonstrate the above implementation of a video rental database using a literal folder of Excel files. This helps separate the distinct skills of designing a database (i.e. deciding the structure) and implementing a particular database system (e.g. SQL Server, Oracle, ...)

I strongly suggest separating the two, as the complexity of learning a particular system often distracts from students learning about and appreciating the theoretical database design skill.