Websites use a thing called the "Hypertext Transfer Protocol" which is where the HTTP at the start of addresses comes from.
This protocol is a standard where the two computers (or phones or whatever) send each other messages about which document to display in your browser. Things like "GET /index" (1) and "GET /tower-bridge.jpg" (2).
And those messages are sent using plain text.
This means that, if someone were snooping on your internet connection, they would be able to read the contents of those messages.
For the most part, this does not matter - because who cares if they can see that you've requested to view the public photo of Tower Bridge that they have on that server, right?
But when it does become important is when it's a site that you have to log in to. And a site where you submit information. Because your username and password, and all the information that you submit, is also sent using plain text. So the snooper can see that as well.
That's where HTTPS comes in - the S on the end is a "secure" variation of HTTP. It uses encryption to make sure that snoopers can't read the contents of the messages that the two computers are exchanging.
However, encryption used to be quite costly in terms of computer power (less so as chips have got faster) so HTTPS wasn't used everywhere. And some sites would offer a HTTP version and a HTTPS version.
Today, there's no real excuse for not using HTTPS - computers are powerful enough to do the encryption quickly and you can get hold of the encryption certificates (3) for free (if your web developer tries to charge you for a basic certificate they are pulling a fast one). But every website still has to deal with the possibility that they might be accessed over HTTP instead of HTTPS - the standard solution is to "redirect" so the server responds with "actually, there's an encrypted version over here and I want you to look at that version instead".
Because of this, browsers now display a warning if a site is available over HTTP. And it's quite a scary warning.
So if you see the warning, and it's just an inconsequential site that you'll never submit any information to, you can probably ignore it. But do ask yourself why they've not updated to HTTPS when it's so cheap and easy to do so.
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1 telling the server that you want to read the homepage
2 telling the server that you'd like to look at the photo of Tower Bridge
3 Encryption certificates contain both the keys to lock and unlock the encryption plus a "chain of trust" which basically proves that the site in question is who they say they are.