Of course 7-speed means 7 cogs on the freewheel. Multiply that by the number of chainrings on the front and that tells you the possible number of different gears that you have.

13/23 Usually means that the smallest sprocket on the freewheel is a 13, the biggest is a 23. I used to have a 7-speed exactly like this. Probably has 13, 14, 15, 17, 19, 21, 23. In the past almost 20 years I've ridden mostly with 7-speed 13/21 freewheels and those work well for the average person in an area that is mostly flat. In digging through my old stuff I also found an old 13/24 freewheel and a 13/19 freewheel (called a straight block).

You can change your gears to be different than 13/23, maybe a lot different. Depending on the age of your bike you might have a freewheel or you might have a freehub with a cassette. You mainly need to buy a new freewheel or cassette with the gears that you want. How much bigger than 23 you can go depends on your rear derailleur.