I've found another analogy that works even better than either of the two above.
Imagine a room (channel) in which people wish to talk to each other simultaneously. If that room only had two people there would be no need to divide the conversations into packets to share the room fairly...they are the only ones in the room, so there is no competition. However fill that room with a lot of people and the "noise" level gets louder. If everyone were talking at the same time, and all spoke the same language, it could be very difficult to hear everything the person you are speaking to specifically is saying due to the noise level, resulting in missed words (lost data packets), and it's also quite possible that you might hear part of someone else's speech nearby and confuse it for that of your party's conversation (cross-talk).
To avoid confusion, people in the room could take turns speaking (Time Division - TDMA), but that would still limit the number of ongoing conversations to only one at a time...not very efficient and there would be a lot of others waiting for their turn. They could speak at different pitches - some with deep voices, some with middle voices, and still others at high-pitched voices (Frequency Division - FDMA). This would allow several conversations to take place at once, but again there is the possibility of it getting too noisy to the point where again you would have lost packets and cross-talk. But what if you all spoke unique and completely different languages instead (Code Division - CDMA)?
I'm sure most of you have been in a situation where there was a conversation nearby in a different language...you take notice at first, but soon the other conversation becomes background noise that isn't confusing you while having your own conversation since you can't understand it anyway. Your brain simply ignores it. CDMA is analogous to the last example where people speaking the same language can understand each other, but other languages are perceived as noise and rejected.
Similarly, in radio CDMA, each group of users is given a shared code. Many codes occupy the same channel, but only users associated with a particular code can communicate. So each cell phone is given it's own code and all communications to and from that cell phone are broken into small packets of data, each with a header that contains that code. Analog waveform of sound from the microphone is encoded (AtoD), into a continuous string of digital data as a series of 0s and 1s. Then that streaming data is broken or portioned into smaller packets of data, perhaps 32K bits per packet, for instance, and sent off to allow them to travel quickly as multiple packets traveling individually and independent of one another at the same time.
Those packets all have starting and ending marks, and each ending mark to one packet lines up sort of like puzzle pieces, with only one other packet's beginning...the one that's next in line. By each packet having the unique perfect lock-key connection to only the next one in line, it allows the packets to travel at different rates of speed and along completely different paths, totally irrespective of one another. They are then collected together at the receiving end, and by using the data contained in the headers they can be sorted into the right order, placed back end to end, decoded (DtoA), back into the analog audio waveform and sent to the speaker as essentially continuous sound.
As those packets are sent out, all other devices listening for data that belongs to them will be looking at only the headers (a very small piece of data), and if the headers aren't properly addressed or coded with the specific code that belongs their own specific cell phone, it's perceived as noise and simply ignored since it needs to know the code in order to decode it into something it can understand. This both allows transmission of massive amounts of data from many multiple sources and to many multiple destinations, and allows massive amounts of irrelevant data to be quickly identified and ignored on the fly by those for whom the data wasn't intended.