<Slider {...settings}>
        {this.state.featuredMovies.map(movie =>
        <div  className="" key={movie._id}>

           <Card inverse style={{padding: "10px", width: "90%"}}>
        <CardImg  src={`/files/${movie.thumbnail}`} alt="Card image cap" />
        <CardImgOverlay className="movie-list-overlay">
          <CardTitle>{movie.MovieName}</CardTitle>
          <CardText>{movie.Description}</CardText>
          <CardText>
            <small>
            <a href="watch">
                    <Button className="btn-fill btn-movie " color="primary" onClick={movie}>
                      Watch  
                    </Button></a></small>
          </CardText>
        </CardImgOverlay>
      </Card>
        </div>
        )}
      </Slider>

<script src=".6.3/umd/react.production.min.js"></script>
<script src=".6.3/umd/react-dom.production.min.js"></script>

回答如下：

你的onClick需要成为一个功能

<Button onClick={() => this.doSomething(movie)} />

然后，您可以访问该功能中的电影值

const doSomething = (movie) => {
  //Do some stuff with the movie
}