Most email programs display a received attachment as an icon in your email, so that you can open the file by double-clicking directly on the icon. However, the file is actually stored in some folder specified in your program configuration settings. Therefore, it is frequently useful to have a shortcut to that folder somewhere convenient on your desktop so you can open it in one click and access any files attached to incoming email.
It’s a good idea to check your attachment folder occasionally to see what is in it, sorting it by date to see the most recent attachments and by size to see the largest files. If you get a lot of email, particularly from mailing lists, you can easily collect several megabytes of attachments without noticing. If you have a large drive of 100 GB or more you may decide you don’t need to worry about attachment sizes at all.
If an attachment is an executable program, then you shouldn’t run it unless it is sent by someone you trust and you were expecting it, since it could contain a virus. If you are running a virus protection program, then make sure it is set to scan files arriving by email and it should keep you secure if you keep the virus database updated. If the attached file is a common program or utility that you want to use, then you should find a known, trusted web page or other source on the Internet and download it from there.