Your friend, your mum, your boss or worse, your wife, calls on you WhatsApp while you are in an important meeting. You can't take the call and since you muted your phone, you let it ring, implicitly conveying to the caller that you are not in a position to take the call. Now since they didn't get you, they send an instant message asking where you are. You see it, but cannot respond. Now, what happens in your correspondent's mind may disturb things: you didn't take the call but you did read the message; so you must be hiding somewhere!
The problem here is that your correspondent had a way to know you read the message - the blue ticks, called read receipts. In WhatsApp, when someone sends a message, a single gray tick appears upon successful dispatch on the network. Once the message reaches the recipient's phone, a second gray tick appears.
Once they read (meaning they opened) the message, the ticks turn blue.
These blue ticks force you to respond to messages immediately lest your correspondents believe you are ignoring them. It is better for your privacy that they do not get notified about that. Fortunately, WhatsApp offers a way to disable it.
Select the menu, then Settings, then Account, and finally Privacy. Scroll down to "Read receipts" and un-check them.
Note that when you disable them, you are also forsaking your ability to be notified about others' actions too. Note also that even if you disable read receipts, they remain enabled and are always sent in group chats. However, for the latter, your privacy is not much at stake as the blue ticks appear only when every person in the group has read the message.
In other instant messaging apps, these ticks are at work as well. But the read notification may take other forms. For instance, in Line, it simply writes "Read" followed by the time it was read. More intrusive!