Broken Modem is a reference to an internet Modem/box. because the internet box is broken, It means that there is a large amount of lag, as the client (player) computer is having trouble getting the data from the host server over the stuttering internet. This shows itself in the item trough the following effects:
The client computer has trouble getting the inputs of other players over the broken internet, meaning the other clients freeze in place and look like they aren't moving, as the computer isn't getting the inputs fast enough to show them. (slows enemies, items, and tears)
The client computer gets the host's or other clients' inputs twice, as the client computer can't send the acceptance trigger to the host server fast enough. (double items)
If this item is rerolled (D4, etc.) while the freezing effect is taking place in a room with enemies, those enemies will remain frozen permanently as long as Isaac remains in that room, making it a matter of time before the room is cleared. This includes bosses.