25-622 is the ETRTO/ISO designation of the tire.

Tire width = 25 mm
Rim nominal diameter = 622 mm

1 inch = 25.4 mm

You must buy a 622 mm nominal diameter tire.

You can buy the same width or a different width tire. If you want to buy a tire with a different width than the old one, you have to measure the inside width of your rim. When you know this, you can look up the allowed tire widths for your rim.

Read this article.