Bitcoin is held in addresses that look like this 13xQrs3e5XjynvShp75A8GDSnz1zJT5H1x
The same address can also be shown as a QR code like this.
To receive Bitcoins to your Ledger hardware wallet you open the wallet and press the receive button this will show the Bitcoin address and the QR code. The Bitcoins sent to this address you will own and have access to spend. If you have Bitcoins in an exchange when you withdraw it will ask for an address to withdraw to and that is where you will put the address created in the above process.
The balance in this address can be found in the open blockchain, the link below shows what it looks like
These addresses are called public addresses (compare it to your bank account number) and you can own multiple of them on the same hardware wallet. For added privacy once an address is used the next time you press receive it will be a new address, you still can receive from the original address but it is recommended to use a new address.
To spend the bitcoins in the address you will need a unique private key linked to the address (like a password). The hardware wallet will manage your keys so all you need to remember is the pin code to spend (and always be sure to have a safe backup of the 24 word seed created when setting up the ledger as this is the only way to recover if you lose your device)
To send using your Ledger Software press the send button, enter the amount in BTC to send (eg 0.002) enter the address to send to ( eg 13xQrs3e5XjynvShp75A8GDSnz1zJT5H1x) then press send, you will then need to confirm this on your device.
The basic steps are similar on mobile devices, you can use the camera on the mobile to scan the barcode of the address you want to send to which makes it easier than trying to type a long address, it also eliminates errors in incorrectly typing the address. Check addresses carefully as you will not be able to get a refund if sent to an incorrect address.