Under the Nash equilibrium, a player does not gain anything from deviating from their initially chosen strategy, assuming the other players also keep their strategies unchanged.
While the link also has an example
Imagine two competing companies: Company A and Company B. Both companies want to determine whether they should launch a new advertising campaign for their products. If both companies start advertising, each company will attract 100 new customers. If only one company decides to advertise, it will attract 200 new customers, while the other company will not attract any new customers. If both companies decide not to advertise, neither company will engage new customers. The payoff table is below:
Company A should advertise its products because the strategy provides a better payoff than the option of not advertising. The same situation exists for Company B. Thus, the scenario when both companies advertise their products is a Nash equilibrium.
It is clearly that if company A keep their initial strategy (advertising products), they will benefits regardless the decision of company B. But why in the definition, they said assuming the other players also keep their strategies unchanged? from my understanding, the company A can get benefit by keep advertising and do not care the action of company B.