Cell Phones (also known as mobile phones) are media devices mainly used for wireless communication.
Cell phone communication is a way of talking to someone when you are distant from their location. It involves sending your voice to another cell phone over a network involving many cell phone transmitters. When people are out of range of any towers, they have no signal and are in what is referred to as a "dead zone."
For demigods, at least the mortal children of the Greek gods, "cell phones transmit a message that says 'Hey, I'm right here!' to monsters," as Percy Jackson says. Using a cell phone for communication is extremely dangerous because monsters are attracted to demigod voices being sent through the air using cell phones. This was the result of a spell cast by Lamia, a daughter of Hecate who had her children killed by Hera and transformed into a monster by the goddess. As a result, most demigods communicate via Iris Messaging which monsters cannot detect or track.
Percy remarks that they are going on a quest with no supervision, not even a cell phone, as calling from one is like sending up a flare to monsters.
In the picture of Annabeth Chase's trunk, she has a cell phone that is off at all times.
Annabeth owns a cell phone, being one of the few demigods to do so. During the Battle of Manhattan, demigods pick up a random cell phone from sleeping mortals which they use to contact the demigods who own their own cell phones, and before discarding it to avoid monsters tracking them to their exact location. They used this to keep track of enemy movements and actions. Sally Jackson gave Percy her phone in the case of an emergency during the Battle of Manhattan.
Percy Jackson also wonders if he should borrow Annabeth's phone to talk to Rachel Dare, but decides not to, because he is worried that Annabeth will get angry with him.
Annabeth lends her cell phone to Piper McLean, but asks for Piper to leave it as a secret. Piper uses it to contact her father Tristan McLean, but Piper's call is unsuccessful, instead going to Tristan's secretary, Jane. During the call, Piper learns that her father has disappeared, captured by the giant Enceladus.
Chiron claims that travel and communication also do not work for any of the demigods: Iris Messages and cell phones don't work, and Camp Jupiter has not communicated with Camp Half-Blood in weeks. Chiron also mentions that campers have been randomly disappearing after looking into the woods. Rachel, despite being mortal, also cannot place calls.