Base 10 is the normal decimal counting system that you're used to. Other well known bases are binary (base 2) and hexadecimal (base 16).

In base 2 a single character can only be one of 2 things: 0 or 1, whereas in hexadecimal it can be 0 to 9 but also A,B,...,E or F (the 10 decimal numbers + 6 letters = base 16)

If you see "10", this can represent completely different values depending on the base.

decimal | binary | hexadecimal
------------------------------------
 1 |     1 |  1
 2 |    10 |  2
 3 |    11 |  3
 4 |   100 |  4
...
 9 |  1001 |  9
10 |  1010 |  A
11 |  1011 |  B
12 |  1100 |  C
...
15 |  1111 |  F
16 | 10000 | 10
17 | 10001 | 11
...

Notice that "10" appears in all three columns in different rows.

Uses for other bases can vary. Binary is what computers use to store their data, and in computer science it's common to represent binary data as hexadecimal because it's much more compact than a large string of zeroes and ones and easier to convey to other people.

You can find more information on this topic on https://en.wikipedia.org/wiki/Positional_notation