Labels are like folders that help you organize your mail, only better! The reason labels are better than folders, is because you can apply more than one label to an email. You can create labels for anything you want.
To create a label, click on "More" in the navigation panel on the left side of your inbox.
Then click on the "Create new label" link at the bottom of the navigation panel.
You should now see a window that asks you to name your new label, and it gives you the option to nest it under an existing label if you wish. When you are finished, you can click the "Create" button.
Now your label should show in the left side navigation panel. If you mouse over your label name, you'll see a little drop down arrow. When you click the arrow, you will see a variety of options, including one to choose a color for your label.
To label an email, either select the email in the inbox list, or open the email and then click on the little label icon that appears across the top of the page. You can then choose which label(s) you'd like to apply to that email. Click "Apply" when you are finished.
Your email will now show the label name across the top.
You'll notice the label name now shows up on the email in the inbox list as well.
You can also drag an email from the inbox list directly to a label name in the left side navigation panel. This will remove your email from the inbox list and place it under that label (you can still find it in searches and in the "All mail" list). If you click the label name in the left side navigation panel, it will show you all the emails you have labeled with that name.