When a dialog is already established between two user agents and then to make any change in the session characteristics is achieved by sending the INVITE message. Since session was already in place and this is the second INVITE, that's why it is known as re-INVITE. This re-INVITE is nothing but an INVITE message with the same Call ID and From header field.
When an ongoing call put on hold, originator of hold sends the INVITE message to the other end and says media will not be transmitted.
Again when originator who earlier has put the call on hold decides to resume the call, again sends INVITE message and informing to other end that media transmission is resumed.
Due to mobility, IP address of the user agent may get change, for an ongoing call , UA would have to send INVITE to other end with the update contact URI and SDP information.
This is all about what I know on INVITE message.