Similar to sending an Email alert, salesforce provides another way to notify its user in its own platform. Suppose there is a business process where you do not want to send an email,but instead you want to send them a notification on desktop/Mobile. For this, Salesforce has provided a tool which is custom notification. 

Custom notification can be automated to send to the intended user/group using process builder, for that you would have to do the following. 

1. Create a Custom Notification in Salesforce.
2. Create a process which sends the notification.

To create a custom notification you have to do the following. 

1. Click on the Gear icon on the right hand top corner and click on setup
2. Type Custom notifications in the quick find box and click on custom notification

3. Click on the new button and fill in the information given below.
   1. Custom Notification Name: Opportunity Closed Lost
   2. API Name: Opportunity_Closed_Lost
   3. Desktop: checked
   4. Mobile: checked

4. Click on save

You have now created a custom notification that you can be used in the process builder.

To trigger this notification we now need to create a process builder and define a criteria i.e when to send this notification to the intended user. In our case we would use an existing process builder that we have used to send an email alert. 

1. Click on the gear icon on the top right hand corner and click on setup.
2. Type process builder in the quick find box and click on the process builder. 
3. Select the previously created process: ‘ Opportunity won’
4. Click on clone and enter the description: ‘Custom notification on closed lost’ and click on save. This will make a new version of the existing process and you can activate and deactivate older versions of the process if required. 

5. Click on the next Criteria node and Define the Criteria with the following details.
   1. Criteria Name: Opportunity Closed Lost
   2. Criteria for Executing Actions: Conditions are met
   3. Set Considitions: 
      1. Field = stage
      2. Operator = Equals
      3. Type = Picklist
      4. Value = Closed Lost

6. Select Conditions:  All of the conditions are met (AND)
7. Click on save.

8.  After saving the Criteria, click on the immediate action and select Action type:Send Custom Notification
9. Enter the following details in the action.
   1. Action Name: Account Owner Notified
   2. Notification Type: Opportunity Closed Lost
   3. Notification Recipient: Owner >[Opportunity].Account.OwnerId
   4. Notification Title: {![Opportunity].Account.Name}
   5. Notification Body: 

Opportunity with Account {![Opportunity].Account.Name} was closed lost

Amount: {![Opportunity].Amount}

10. Target Object:  Opportunity Object that started the process.

10. Click on save 
11. Activate the process by clicking on the activate button.

Below are the test result 

When an Opportunity is closed lost, the account owner receives a notification.

Below is the Notification body.

For More Examples refer : Automate you Business Process