An admin account is a "super user" account in Linux. It's used generally to update the system or add applications. This in itself, is simplified within the system, by using a user account and then asking for the user password. This method is making you a user of sudo, another way of simplifying Linux for the masses.
You should always use a user account for general computing within a Linux system. Using an admin account, is a quick way to make your system unusable if you don't know what you're doing, or indeed just make an error.
Linux is unforgiving at admin level. If you tell it to delete a file, it will do so, not ask for confirmation like Windows.
When using a user account to install applications, (programs), you simply select what you want from "Ubuntu software" and click install. As already mentioned, you will need your user password to complete the task.
You can also install software via the command line, but that's a whole new story.