Database is collection of data in a most efficient way so that insertion, update ,deletion ,and selection. To perform most common operation there are lots of database available over internet to fulfill different purpose.
Database is important part of our project and as a software engineer or developer or even if you are computer science student you must know as much so that you can perform basic and medium level query easily.
Database schema is refer to high level data collection view not details view.
Like suppose you are going to design database schema of colleges then database schema includes all table with fields name , key attribute, and relation between tables.
You may think database schema as ERD but not exactly same because in ERD diagram you mention each attribute, derived attribute, relation with diagonal same like that but this is not included in database schemas.
Here is official definition of Database schema- The term "schema" refers to the organization of data as a blueprint of how the database is constructed (divided into database tables in the case of relational databases). The formal definition of a database schema is a set of formulas (sentences) called integrity constraints imposed on a database.
Here is some common tool for Database Diagram Design