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Channels feel counterintuitive, but they do make sense eventually. Using an easy lightning node wallet like Phoenix or Zeus can sometimes make it simple.
Here's what made it click for me.
When you use something like Phoenix where the node is on your phone, you often only have one channel and that channel is with the node run by Phoenix.
Think of them as your gateway to the rest of the lightning network. Every payment you send will go through your channel with them. Same for every payment you receive.
Mostly, you can think of a lightning channel as just a 2 of 2 multisig where you and your channel partner each have one key.
When you open a channel with Phoenix you deposit some bitcoin into this multisig. Phoenix doesn't have to deposit any. So let's assume they don't.
If you kept track of who owns how much of the bitcoin in the multisig, you would say you own it all and Phoenix doesn't own any.
Now, when you send a payment you agree that some of the bitcoin in the multisig belongs to Phoenix...if (and only if) Phoenix sends the same amount to the destination you specify.
If they prove they have done so, you agree that some of the bitcoin in the multisig now belongs to Phoenix. But as long as the channel is still open (meaning as long as there is still a utxo controlled by this 2 of 2 where you and Phoenix each have a key), no bitcoin has actually left the multisig. All that happened is that you and Phoenix both agreed that some of it belongs to Phoenix now.
You could keep sensing lightning payments and asking Phoenix to send bitcoin on your behalf up to the point where all the bitcoin in the multisig is now owned by Phoenix. At that point Phoenix isn't going to send any bitcoin on your behalf because they have no guarantee that you will reimburse them.
If you receive a payment from someone else through your channel with Phoenix, Phoenix would agree that that amount of bitcoin in the multisig belongs to you. And you could keep receiving like that until you both agreed that all the bitcoin in the multisig belonged to you. At this point you couldn't receive any more because even of whoever wanted to pay you gave their bitcoin to Phoenix, you have no guarantee that Phoenix will give it to you.
The bitcoin in the multisig is what people call liquidity. When Phoenix makes a payment on your behalf, the bitcoin is actually moving through a series of relationships where people have these multisigs and agree to adjust how much each party owns.
This was pretty long winded, but I've never really liked any of the analogies people use, so I thought I'd just try to describe what is actually happening.