To receive bitcoins, open the Receive tab. Receiving address is your Bitcoin address and it is something like your bank account number. Thus, if you are buying bitcoins by bank transfer or with your credit card or simply wish to receive bitcoins from a person, you should indicate this address for payment.
Upon receiving a payment, Electrum will display a notification. Althouh the risk of Bitcoin double-spends is extremely low, if you do not personally know the person sending you bitcoins, allow the Bitcoin network to confirm the transaction at least once (6 confirmations is often considered the most secure threshold).