Price Impact
How much a trade moves the market price by itself, simply because of its size relative to the liquidity available.
On an order book, impact is the cost of consuming the best-priced resting orders and then reaching worse-priced ones further down the queue. On an automated market maker it is the movement along the pricing curve as the pool balances change. Impact grows with the ratio of trade size to available depth, which is why the same order is cheap in a deep market and expensive in a shallow one. Traders reduce it by splitting orders over time, routing across several venues, or arranging the trade over the counter.
In practice
The same order that barely moves a deep major-asset market can move a thinly traded market by a wide margin, because there is little resting size near the quote.
The common misunderstanding
Price impact is not a fee paid to anyone; it is the cost of exhausting the cheapest liquidity and having to reach the next level.