Software engineering is an engineering discipline that’s applied to the development of software in a systematic approach (software process). It’s the application of theories, methods, and tools to design build a software that meets the specifications efficiently, cost-effectively, and ensuring quality. (time - budget - quality)
Not applying software engineering methods results in more expensive, less reliable software, and it can be vital on the long term, as the changes come in, the costs will dramatically increase.
Programmer can build softwares alone. But things turn complicated when you add more people and want to get it done in time. Programming means getting a program working. You have a problem to solve, you write some code, you run it, you get your answer, you’re done. That’s programming, and that's difficult enough by itself.
https://www.youtube.com/watch?v=EiKK04Ht8QI
But what if that code has to keep working, day after day? What if five other programmers need to work on the code too? Then you start to think about version control systems, to track how the code changes over time and to coordinate with the other programmers. You add unit tests, to make sure bugs you fix are not reintroduced over time, not by you six months from now, and not by that new team member who’s unfamiliar with the code. You think about modularity and design patterns, to divide the program into parts that team members can work on mostly independently. You use tools to help you find bugs earlier. You look for ways to make programs as clear as possible, so that bugs are less likely. You make sure that small changes can be tested quickly, even in large programs. You're doing all of this because your programming has turned into software engineering.
Software engineering is what happens to programming when you add time and other programmers. - Russ Cox
Reference

Engineering https://www.youtube.com/watch?v=btGYcizV0iI
How to become an engineer https://www.youtube.com/watch?v=77xMVKOEZ5g
Engineering Ethics https://www.youtube.com/watch?v=5KZx81crb48
Software Engineering https://www.youtube.com/watch?v=O753uuutqH8
Next: Software process
