With wordpress it is pretty common task to keep all your plugins up to dates. and while performing this update task using wp admin it prompts you with FTP settings screen.
Whereas the expectation is the wordpress should update it without FTP by performing this in background.
Also in some hosting environments ftp is often blocked.
The way to get away of this FTP prompt is by changing the file permissions of wordpress directory. This happens when wordpress is setup using root user and being executed by Apache user.
You can resolve this issue by switching the wordpress directory permissions using chown command via SSH.
sudo chown -R apache:apache /path/to/web