What are ACID properties in databases and why are they important?

I'm learning about database management systems and frequently come across the term ACID properties. I understand that ACID stands for Atomicity, Consistency, Isolation, and Durability, but I'm not sure what each property means or why they're essential for database transactions.

Can someone explain each ACID property with simple examples and describe how they help ensure data integrity and reliability in relational databases? I'd also like to know which databases support ACID transactions and when they are most important in real-world applications, such as banking or e-commerce systems.