EDIT: This info below is now out of date. You can upload more or less anything you want in terms of images and sizes. We convert the original image to a lighter format if we need to. Don’t worry, be happy.
The current default for a maximum individual image size on posts is 3 MB. If they are larger than that then it should give back a nice upload error, or alternatively it will just look at you confused and you’ll think it has hung. When an image is uploaded smaller thumbnails are shown in the posts, so for mobile users the topics load faster. The original can always be accessed by clicking into the image. You can have as many 3 MB images in a post as you like (well, 65,536 but basically a lot).
If you have the odd image to upload that is larger than 3 MB then an easy way to upload is just to load it up in your default Windows/Mac viewer and then CTRL+C copy - you can then paste it into a post editor box and it’ll make a JPG for you automatically.
If you have lots of large images then it might be worth either saving them originally smaller before uploading or batch converting them with an OS tool first. @EinsteinEP likes xnconvert, or old stuff like Ifranview or ImageMagik for command line stuff works as well. If you have a nice Windows or Mac free image batch converter tool that you like then let us know.
The 3MB limit was picked to allow @BeachAV8R to keep some money to send Kai to college rather than spend it on storage, but it’s easily tweakable if people feel they want it larger and that limit is too low. Or, I guess, we just want less people at college. Happy either way.