Because it is:

1. Easy to explain. (Its essentially a game, the "imitation game")
2. Intuitively plausible as a metric.
3. The idea of "people v.s. AI" is very marketable.
4. At the time we thought that we can analyze cognition strictly in terms of input/output (per behaviourism). Cognitivism, embodied cognition, developmental cognition are all sub-fields that have a right to challenge the Turing Test, but they weren't developed at the time of Turing.

Of course it also helps that Turing is a very important figure in AI/CS,

Because it is:

1. Easy to explain. (Its essentially a game, the "imitation game")
2. Intuitively plausible as a metric.
3. The idea of "people v.s. AI" is very marketable.
4. At the time we thought that we can analyze cognition strictly in terms of input/output (per behaviorism). Cognitivism, embodied cognition, developmental cognition are all sub-fields that have a right to challenge the Turing Test, but they weren't developed at the time of Turing.

Of course, it also helps that Turing is a very important figure in AI/CS.