In forex trading, a "pip" is a convention which provides an approximate way of comparing profits from different trades while ignoring the trade volume (and thus ignoring the actual cash profit). It is defined as a price movement of 0.0001, except for JPY pairs (and HUF) where it is defined as 0.01.
The notion of a pip works in fx because (a) the most heavily traded pairs are all xxx/USD, xxx/JPY, or xxx/CHF, and (b) the USD/JPY rate is close to 100 and the USD/CHF rate is close to 1. If AUD/USD or GBP/USD rises by 100 pips, then it has changed in price by 1 US cent. If GBP/JPY rises by 100 pips, then it has moved by 1 yen, and that is close to 1 US cent. Similarly, if EUR/CHF rises in price by 100 pips then it has moved by 1 Swiss franc, which is again close to 1 US cent.
But the notion of a "pip" works less well on a symbol such as EUR/GBP. A change of 100 pips on EUR/GBP is a change of 1 British penny, which is - currently - worth about 30% more than 1 US cent. Therefore, a trader who makes 100 pips profit on EUR/GBP has made a substantially larger cash profit than someone who has traded the same volume (of euros) on e.g. EUR/USD.
In other words, in fx the notion of a pip is a broad and approximate way of comparing trades. It would become a lot less useful if, for example, the USD/JPY rate went up to 200, or down to 50.
Outside of fx, there is no consensus on what the "pip" sizes should be for instruments (and the term "pip" is relatively rarely used by traders). For example, different people will define a pip on spot gold variously as 1.00, 0.10, 0.01, or even occasionally 0.05. There is no consensus in the same way as for forex pairs (and there is certainly no "correct" or "official" definition).
Our systems currently define the pip size on gold as 0.10 and on silver as 0.01. This means that the cash profit when trading 1 lot of gold or silver (using most brokers' contract sizes) is relatively close to the cash value when trading 1 lot (i.e. 100K) of a forex pair. Other non-forex instruments are defined as having a pip size of 1.00, except for a few oil and index contracts.