"What does 300dpi mean?" - This is a popular question in the print industry. The 300dpi stands for "dots per inch" and refers to the resolution of printing. The same way you may look to purchase a television with 1920x1080 resolution vs a 4k television that has 3800 resolution is the same way print production works.
In the high-edn offset print method, 300dpi is the highest resolution needed to achieve a flawless print job. Some have argued, "Well, i heard there is 600dpi so that's better, right?" Not quite! The 600dpi methods are printing digitally and digital is 6-8 times lower quality than offset.
Digital is a similar process to your home or offices printing machine. It prints in horizontal lines and requires more pixels per inch just to look decent. Offset print service requires lower dpi because it is printed using metal film plate negatives, similar to professionally developed photography.
When setting up your artwork in popular high-edn software like Adobe Photoshop, it is always best to first set your canvas size to 300dpi in order to create a super high quality file that will be reproduced in HD print quality. Designing in a lower dpi and then resizing later will cause quality loss to your artwork. If you design in anything higher than 300dpi it will not print any better. The 300dpi resolution is the standard in printing.