Why is it when someone sends email to me, it does not show up in my IN-BOX until the next day or later?

When you send an email, it doesn't go directly from their outbox to your inbox. The way the Internet works is a lot like the Post Office actually. When you send a message, first the message looks to see if the recipient is "local" and is known by your ISP. If it is, it gets redirected to them right there, just like if the person you're sending an actual piece of mail to is in the same zip code as you. If not, it goes up a level of "localness" and sees if any servers know who the recipient is. If so, again, the higher up server direct the message to the lower server which then passes it along to the other user, just as mail is sent to a regional post office, and then to the appropriate zip code if the person you're sending to is in a different one (like locally for me, mail gets sent to a different city 30 miles away, even if the mail is going to someone else in my city, but in a different zip code). And if not, that server turns to yet another level up. The process is repeated until someone knows where your email is supposed to go.

In short, that means that somewhere along the line, one of the servers is slow. If it happens every time, it might be your ISP. Conversely, if it's only from a certain individual it happens every time, it might be theirs. But that'd be just a guess though.