Look at the IP address as a mail address.
Let's say you live at Main street 24 in a town called Mytown, in the State of Mystate, in the county Mycounty in the country, let's say, the USA.
If this address is a private home, then you and you alone will have this address.
If someone from, let's say, Japan should send you a letter and uses the above address, that letter will finally end up in your mailbox!
Even if you are not at home (similar to your computer not connected to the Internet) that address does exist. If you are not at home (computer is not online and connected to the Internet) you will not be able to take out the letter from the mailbox and read it. As soon as your computer is online, a certain IP address will be assigned to your computer via many hubs, switches and gateways (like post offices in the mail world) and your emailbox will be connected to that IP address so that email with your email address will finally be delivered to that IP address.
As long as your computer is not online, you will not be able to open the email that was sent to you via any mail server, regardless if you use a mail client program such as outlook or use a web browser and get your mail from f.i. Gmail.