To help you think on the right terms, consider an analogy: A text document on a computer versus a sheet of printed paper. When I have a text file open on my computer, I can make whatever change I want. However, once I print, the text on that paper is unchangeable.

A JPEG image is made of rows of pixels. Apart from some metadata that can give us some information about who created the image and how it was created, all you get are pixels. So, the image itself can't tell whether a pixel is creating a line, a photo, or text; it's just displaying pixels in a grid.

A PSD, however, contains data about the individual objects that make up an image. That's why you're able to open a PSD and edit things.

If you want to edit a JPEG, it is possible, but doing so is as cumbersome as making edits to printed sheet of paper. If I wanted to edit a printed document, I would either have to retype or scan it in and use OCR to get editable text before I could edit that text.

As Scott says, you have to paint over the old text and replace it with new text. However, before you do that, I find it useful to recreate the existing text in Photoshop. So, if you have a single line of text, remake that line, figuring out the font face, size, weight, kerning, and color so that you can put it over top of the old text and match it exactly. Then, delete your old text. Finally, retype the text.