Background information

Gmail uses labels instead of a traditional folder structure.  The advantage is that you can add multiple labels to a single email.  With folders, you could only put an email into a single folder.  Google's help documentation has an explanation of labels: https://support.google.com/mail/answer/118708?hl=en

If you have a large number of Labels, it may be hard to navigate through the list.  It is possible to hide little-used labels (see below).

Move labeled mail out of the inbox

By default, if you apply a label to an email, the email will remain in your inbox.  If you'd like to apply a label and remove the email from the inbox, select the email (or open it) and click on the folder icon above your email listing.  Select the appropriate label and it will be applied, then the email will be removed from the inbox.

Hiding Labels

1. Go to Settings → Labels 

2. Choose which labels to show/hide
   Once hidden, you can easily find emails within the label by using Gmail's search using the following pattern:  label: <Your-label-name>.  For instance, if I wanted to find all the email I had labeled as "Project X", I would type label: Project X in the Gmail search bar.