I would first start by reading a little bit about databases before you actually start working with them, or at least have a book next to you as a reference. There are several places on the internet where you can download free ebooks about MySQL to get up to speed :)
Generally speaking, mysql(-server) is an environment that can hold different databases. By default, it only has a little bit of data in a few databases that are required to work correctly and besides the users that are necessary for access rights, you're rarely going to access the existing databases. You can create your own database for example by
$mysql -u root -p // to log in your database environment as 'root'
mysql> CREATE DATABASE people;
mysql> USE people;
mysql> CREATE TABLE names (
` id int(4) unsigned not null primary key,
` name varchar(32) not null
With that, you have a new empty database with 1 table that stores names.
Every database can have multiple tables, and ever table can have multiple columns and every column can have multiple values, links, binaries, etc.
To see what you are doing when you're learning, I advise you to install phpmyadmin, which is a web-based front-end for your database. You can easily create databases and see what is going on. It will also give you the queries (mysql strings) that are used for the operations you perform. After installation, just browse to
http://127.0.0.1/phpmyadmin and it'll be a lot easier for you to see what you're doing. You'll also be able to create databases without having to know everything about MySQL.
LAMP is an abreviation for (L)inux(A)pache(M)ySQL(P)HP, which are 4 different environments that are frequently used together to create dynamic websites. This is a bit of a time of change, as many web hosters are currently switching to Nginx instead of Apache, and MariaDB instead of MySQL. Only in later stages of development, you will start to see any differences between them. They're all there with the same purpose. But if you already have MySQL installed on Linux, you already have half of the LAMP stack installed.
You can always install the rest manually with apt.