Notifications or Email?
You have a number of options available for you for sending notifications to members:
Members can follow other members, content containers (nodes like categories) and content items (like topics) to be notified about content that interests them. For information on how to implement this, see the Following sections for the Content Items and Comments documentation.
Members can choose how to be notified about certain events (if they want to receive an inline notification, an email, both or neither) and you can send them notifications honoring those settings. For example, notifications are sent when someone posts on another user's profile. For information on how to implement this, see below.
You can also manually send an email to a member. For information on how to implement this, see below.
Though all 3 systems interact with each other, it is important not to confuse them: the follow system sends a notification which may be an email. You can also send a notification which may be an email, or you can just send an email.
If you need to send a notification to a user, you should think carefully about whether a notification or an email is appropriate. Generally notifications are best for telling a user about something that has happened that they might be interested in (for example, notifications are sent when someone posts on another user's profile) and emails are best for things which are in response to a specific action, or require action from the user (for example, an email is sent when a product a user has purchased from Commerce is shipped).