"(When we speak about p-adic numbers, p is some specific number, usually a prime, and the digits of the number are 0,…,p-1.) Now we say that two numbers are “close” if their digits are the same for a long way to the left! So the 10-adic numbers 0.03, 0.53, 6.53, 96.53, 196.53, 1196.53, 21196.53,… are getting closer and closer together. "

None the wiser as to what p-adic numbers are.

Wikipedia basically explains it though: two p-adic numbers are considered to be close when their difference is divisible by a high power of p: the higher the power, the closer they are