One common problem with remote hosts is that they sometimes move sites to different folders on the host server. In general, this does not cause obvious problems in Joomla!. However, when you install an extension, you need to be able to write to the "tmp" directory.
On some servers you may only need to provided FTP credentials for installation to complete. Check with your host to determine if this is necessary.
For security reasons, it is best to create a separate FTP user account with access to the Joomla! installation only and not the entire web server.
Note: If you are installing on a Windows Operating System, the FTP layer is not required. It's only needed on Linux servers that are running php as Apache not cgi(fast cgi)
In this case, you might get the error message:
"JFolder::create: Could not create directory"
"Warning! Failed to move file."
If you have the Joomla! FTP layer enabled, you might get the message
"JFTP::mkdir: Bad response, JFTP::chmod: Bad response, JFTP::store: Bad response, Warning! Failed to move file."
The ftp layer is designed as a work around for poorly setup servers.