If you are no longer interested in receiving notifications from a specific account, you can unfollow the account. You can always follow them again at a later time if you wish.
If are looking to disable all notifications, see this article.
From your dashboard, click View Public Profile (below your account name).
Click the Following tab at the top of your profile.
You will see a list of accounts that you are following. Hover your mouse over the green Following button; this will change the button to red and read Unfollow. Click it to unfollow the account.