funds are not moved to your computer. they are on the blockchain.
electrum is just the tool to view and communicate with the blockchain. but you dont need to be permanently connected to 'accept' payment.
the network accepts the payment by confirming transactions into blocks. the blockchain is not in one place, never shuts down it is 24/7 network..
you can view your funds on any blockchain viewer (node/explorer) but only move funds if you provide your private key
your private key is your proof that you have the authority to move funds... all you need to worry about is having the private key to that public address to prove that you are the one thats allowed to spend it, whenever you want to spend it at a later date
wording it another way(fiat analogy)
telling your employers your bank details that are wrote on your debit card. does not mean you can only get paid by having to have your debit card permanently inserted into an ATM. or by having a sleeping bag and sleeping inside the local bank. or by having to log into your online bank and stay logged in
you can get paid whenever.. by whomever and however much they want to pay you..
your private key is like your ATM pin number. dont tell anyone it. but you will need it when its time to spend the funds
Wow thats just the answer I was wanting! thanks! Most reply here are to not beginner friendly I must say haha. Anyway thank you very much for this good explanation.