React js onClick can't pass value to method

Easy Way

Use an arrow function:

return (
  <th value={column} onClick={() => this.handleSort(column)}>{column}</th>
);

This will create a new function that calls handleSort with the right params.

Better Way

Extract it into a sub-component. The problem with using an arrow function in the render call is it will create a new function every time, which ends up causing unneeded re-renders.

If you create a sub-component, you can pass handler and use props as the arguments, which will then re-render only when the props change (because the handler reference now never changes):

Sub-component

class TableHeader extends Component {
  handleClick = () => {
    this.props.onHeaderClick(this.props.value);
  }

  render() {
    return (
      <th onClick={this.handleClick}>
        {this.props.column}
      </th>
    );
  }
}

Main component

{this.props.defaultColumns.map((column) => (
  <TableHeader
    value={column}
    onHeaderClick={this.handleSort}
  />
))}

Old Easy Way (ES5)

Use .bind to pass the parameter you want, this way you are binding the function with the Component context :

return (
  <th value={column} onClick={this.handleSort.bind(this, column)}>{column}</th>
);

There are nice answers here, and i agree with @Austin Greco (the second option with separate components)
There is another way i like, currying.
What you can do is create a function that accept a parameter (your parameter) and returns another function that accepts another parameter (the click event in this case). then you are free to do with it what ever you want.

ES5:

handleChange(param) { // param is the argument you passed to the function
    return function (e) { // e is the event object that returned

    };
}

ES6:

handleChange = param => e => {
    // param is the argument you passed to the function
    // e is the event object that returned
};

And you will use it this way:

<input 
    type="text" 
    onChange={this.handleChange(someParam)} 
/>

Here is a full example of such usage:

const someArr = ["A", "B", "C", "D"];

class App extends React.Component {
  state = {
    valueA: "",
    valueB: "some initial value",
    valueC: "",
    valueD: "blah blah"
  };

  handleChange = param => e => {
    const nextValue = e.target.value;
    this.setState({ ["value" + param]: nextValue });
  };

  render() {
    return (
      <div>
        {someArr.map(obj => {
          return (
            <div>
              <label>
                {`input ${obj}   `}
              </label>
              <input
                type="text"
                value={this.state["value" + obj]}
                onChange={this.handleChange(obj)}
              />
              <br />
              <br />
            </div>
          );
        })}
      </div>
    );
  }
}

const rootElement = document.getElementById("root");
ReactDOM.render(<App />, rootElement);

<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react-dom.min.js"></script>
<div id="root"></div>

Note that this approach doesn't solve the creation of a new instance on each render.
I like this approach over the other inline handlers as this one is more concise and readable in my opinion.

Edit:
As suggested in the comments below, you can cache / memoize the result of the function.

Here is a naive implementation:

let memo = {};

const someArr = ["A", "B", "C", "D"];

class App extends React.Component {
  state = {
    valueA: "",
    valueB: "some initial value",
    valueC: "",
    valueD: "blah blah"
  };

  handleChange = param => {
    const handler = e => {
      const nextValue = e.target.value;
      this.setState({ ["value" + param]: nextValue });
    }
    if (!memo[param]) {
      memo[param] = e => handler(e)
    }
    return memo[param]
  };

  render() {
    return (
      <div>
        {someArr.map(obj => {
          return (
            <div key={obj}>
              <label>
                {`input ${obj}   `}
              </label>
              <input
                type="text"
                value={this.state["value" + obj]}
                onChange={this.handleChange(obj)}
              />
              <br />
              <br />
            </div>
          );
        })}
      </div>
    );
  }
}

const rootElement = document.getElementById("root");
ReactDOM.render(<App />, rootElement);

<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react-dom.min.js"></script>
<div id="root" />

Nowadays, with ES6, I feel we could use an updated answer.

return (
  <th value={column} onClick={()=>this.handleSort(column)} >{column}</th>
);

Basically, (for any that don't know) since onClick is expecting a function passed to it, bind works because it creates a copy of a function. Instead we can pass an arrow function expression that simply invokes the function we want, and preserves this. You should never need to bind the render method in React, but if for some reason you're losing this in one of your component methods:

constructor(props) {
  super(props);
  this.myMethod = this.myMethod.bind(this);
}