If you are not familiar with SSH, the functions and information on this page may be of some help to get you started.
Quick Overview
SSH (or Secure SHell) is a network protocol that allows two devices to communicate and exchange data securely. You can use it to wirelessly access your iPhone. Most commonly this is done with the Terminal.app, that is, through a command line interface. The device does not have to be connected to your Mac; and there is no problem if it is connected.
You can install SSH on jailbroken devices with Cydia (Cydia -> Sections -> Networking -> OpenSSH.)
You will gain direct access to the device's file system.
Connect
If you have a WiFi connection, you should be able to access the phone via SSH from Terminal.app with: ssh root@ (click to copy,) or click Connect... below. This command may take a while - I'd give up after a minute or so. If there is no IP address in the command, or it doesn't work, then you need to find the address yourself; Go to Settings->WiFi and tap on the blue arrow next to your WiFi network. 'IP Address' is the address you are looking for - enter it in the 'IP Address' field below and press the 'Return' or 'Enter' key.
If you get the following message in Terminal:
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@ WARNING: REMOTE HOST IDENTIFICATION HAS CHANGED! @ ...
then, if the IP address above is correct, you can click Fix Warning to have iFuntastic fix that for you. (Or do it yourself: remove the line for from the file ~/.ssh/known_hosts.) Then try to connect again.
Password
The default password is alpine, and everyone knows it. For security, you should change it. You can do that with the Set Password function.
It performs the following steps (which you can do manually as well:)

- ask for a new password
- run openssl passwd -crypt -salt /s <password> in the shell (Terminal)
- copy the resulting string into /etc/master.passwd on the phone (between the first two colons of the root and mobile entries)

No Password
You can click Set Empty Password to keep SSH from asking for your password every time (or do it manually.) This takes the first S out of SSH, so don't forget to change it back! iFuntastic will do the following:

- generate a new rsa key pair for an empty password (ssh-keygen -t rsa -f id_rsa -N "")
- copy the file ~/.ssh/id_rsa.pub to /var/root/.ssh/authorized_keys on the phone
- set the appropriate permissions (chmod 0777 ~/.ssh, chmod 666 ~/.ssh/authorized_keys and chmod go-w /private/var/root.)