What 300 DPI changes
This page is PDF to JPG with the highest quality preselected. Resolution is how many pixels are used for every inch of the page. At 300 DPI, a Letter page becomes an image of about 2550 × 3300 pixels, and an A4 page about 2480 × 3508. At 150 DPI, the middle option, the same page has half the width and half the height, which is a quarter of the pixels.
Those extra pixels are what let you print the page at full size without jagged lettering, zoom into a floor plan, or crop a detail from an illustration and still have it look sharp.
When high quality is worth it
For printing: 300 DPI is the usual reference for photo and commercial printing. If you're printing an invitation, a flyer, a certificate or a magazine page that came as a PDF, this is the setting. For design, too: if the page is going into an editing app or a large presentation, it pays to start from an image with room to scale.
And for reading details: floor plans, sheet music, tables with small numbers and documents with fine print are easier to read when the image has enough resolution to zoom in.
The cost: file size and time
More pixels mean heavier files and a slower conversion, especially on phones and with long PDFs. Pages are processed one at a time so memory doesn't run out, and a progress bar shows how far along it is. If you only want to share pages in a chat, post them on social media or view them on screen, 150 DPI is usually enough and much lighter; you can switch in the same tool.
If an image later needs to be smaller for an upload form, use Compress image. And if you need quality with no loss at all, for very fine text or flat-color graphics, PDF to PNG saves pages without lossy compression, at the cost of bigger files.
Two things worth knowing
First, 300 DPI can't create detail that isn't there. If the PDF is a low-resolution scan or contains small photos, the image will be bigger but not sharper. What always benefits is text and vector graphics, which are redrawn at the chosen resolution.
Second, what counts for printing is the pixel count. If an app shows a different DPI figure in the file's properties, you can set it to 300 without touching the image using Change image DPI. And if you want the photos embedded in the PDF rather than whole pages, pick the Extract images mode in the same tool.