The coins are "stored" in the blockchain.
Electrum holds the keys that can "unlock" your ability to spend bitcoin you have received.
Electrum (and every other wallet) DON'T store coins. They only store keys. That's a common misconception.

In order to "receive" coins, you need NOTHING at all. Just give someone an address.

You need Internet in order to:
1. Monitor your incoming transactions and perhaps get notifications about them.
2. Broadcast transactions a.k.a "send coins"

You don't need Internet to:
1. Receive coins
2. Sign transactions (assuming you will broadcast them later)
3. Create new wallets aka new pairs of keys

I hope I have answered your question. You don't need Internet to receive bitcoin. Coins are stored nowhere. That's not how it works. If someone wants to send you coins, they have to broadcast a transaction and let people (other nodes and miners) know that they have sent the coins. Once you open up electrum you need Internet to "see that you have received the coins".