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1. Exploit the nested loop structure: The first if condition checking for line-breaks becomes true whenever the inner loop terminates. Get rid of the condition and move the statement below the inner loop body:

var size = 8;
var result = '';
for (var i = 0; i < size; i++) {
  for (var j = 0; j < size; j++) {
    if ((j % 2 === 0 && i % 2 === 0) || (j % 2 === 1 && i % 2 === 1)) {
      result += ' ';
    } else if ((j % 2 === 0 && i % 2 === 1) || (j % 2 === 1 && i % 2 === 0)) {
      result += '#'; 
    }
  }
  result += '\n';
}

2. Remove the redundant else if condition: The final else if condition is redundant as it is always true when the first if-condition is false. Remove it:

var size = 8;
var result = '';
for (var i = 0; i < size; i++) {
  for (var j = 0; j < size; j++) {
    if ((j % 2 === 0 && i % 2 === 0) || (j % 2 === 1 && i % 2 === 1)) {
      result += ' ';
    } else {
      result += '#'; 
    }
  }
  result += '\n';
}

3. Simplify the if condition: Your if condition can be expressed in terms of both loop iterators and thereby simplified to (j + i) % 2 === 0:

var size = 8;
var result = '';
for (var i = 0; i < size; i++) {
  for (var j = 0; j < size; j++) {
    if ((j + i) % 2 === 0) {
      result += ' ';
    } else {
      result += '#'; 
    }
  }
  result += '\n';
}

4. Invert the negative if condition: You can get rid of the explicit comparison to zero by switching your if and else statements:

var size = 8;
var result = '';
for (var i = 0; i < size; i++) {
  for (var j = 0; j < size; j++) {
    if ((j + i) % 2) {
      result += '#';
    } else {
      result += ' '; 
    }
  }
  result += '\n';
}

5. Use the conditional ternary operator for terse conditional assignments: You can replace the somewhat verbose if else statements with a single conditional assignment using the conditional ternary operator:

var size = 8;
var result = "";
for (var i = 0; i < size; i++) {
  for (var j = 0; j < size; j++) {
    result += (j + i) % 2 ? '#' : ' ';
  }
  result += '\n';
}

6. Replace the declarative loop with a more descriptive approach: Exploit built-in methods and introduce new named identifiers for self-documenting code:

function createBoard(size, black = '#', white = ' ') {
  let even = (white + black).repeat(size / 2) + (size % 2 ? white : '') + '\n';
  let odd  = (black + white).repeat(size / 2) + (size % 2 ? black : '') + '\n';
  return     (even  + odd  ).repeat(size / 2) + (size % 2 ? even  : '');
}

console.log(createBoard(8));

1. Exploit the nested loop structure: The first if condition checking for line-breaks becomes true whenever the inner loop terminates. Get rid of the condition and move the statement below the inner loop body:

    var size = 8;
    var result = '';
    for (var i = 0; i < size; i++) {
      for (var j = 0; j < size; j++) {
        if ((j % 2 === 0 && i % 2 === 0) || (j % 2 === 1 && i % 2 === 1)) {
          result += ' ';
        } else if ((j % 2 === 0 && i % 2 === 1) || (j % 2 === 1 && i % 2 === 0)) {
          result += '#'; 
        }
      }
      result += '\n';
    }
   

2. Remove the redundant else if condition: The final else if condition is redundant as it is always true when the first if-condition is false. Remove it:

    var size = 8;
    var result = '';
    for (var i = 0; i < size; i++) {
      for (var j = 0; j < size; j++) {
        if ((j % 2 === 0 && i % 2 === 0) || (j % 2 === 1 && i % 2 === 1)) {
          result += ' ';
        } else {
          result += '#'; 
        }
      }
      result += '\n';
    }
   

3. Simplify the if condition: Your if condition can be expressed in terms of both loop iterators and thereby simplified to (j + i) % 2 === 0:

    var size = 8;
    var result = '';
    for (var i = 0; i < size; i++) {
      for (var j = 0; j < size; j++) {
        if ((j + i) % 2 === 0) {
          result += ' ';
        } else {
          result += '#'; 
        }
      }
      result += '\n';
    }
   

4. Invert the negative if condition: You can get rid of the explicit comparison to zero by switching your if and else statements:

    var size = 8;
    var result = '';
    for (var i = 0; i < size; i++) {
      for (var j = 0; j < size; j++) {
        if ((j + i) % 2) {
          result += '#';
        } else {
          result += ' '; 
        }
      }
      result += '\n';
    }
   

5. Use the conditional ternary operator for terse conditional assignments: You can replace the somewhat verbose if else statements with a single conditional assignment using the conditional ternary operator:

    var size = 8;
    var result = "";
    for (var i = 0; i < size; i++) {
      for (var j = 0; j < size; j++) {
        result += (j + i) % 2 ? '#' : ' ';
      }
      result += '\n';
    }
   

6. Replace the declarative loop with a more descriptive approach: Exploit built-in methods and introduce new named identifiers for self-documenting code:

    function createBoard(size, black = '#', white = ' ') {
      let even = (white + black).repeat(size / 2) + (size % 2 ? white : '') + '\n';
      let odd  = (black + white).repeat(size / 2) + (size % 2 ? black : '') + '\n';
      return     (even  + odd  ).repeat(size / 2) + (size % 2 ? even  : '');
    }
   
    console.log(createBoard(8));
   

function createBoard(size, black = '#', white = ' ') {
  let even = (white + black).repeat(size / 2) + (size % 2 ? white : '') + '\n';
  let odd  = (black + white).repeat(size / 2) + (size % 2 ? black : '') + '\n';
  return     (even  + odd  ).repeat(size / 2) + (size % 2 ? even  : '');
}

console.log(createBoard(7));

function createBoard(size, black = '#', white = ' ') {
  let even = (white + black).repeat(size / 2) + (size % 2 ? white : '') + '\n';
  let odd  = (black + white).repeat(size / 2) + (size % 2 ? black : '') + '\n';
  return     (even  + odd  ).repeat(size / 2) + (size % 2 ? even  : '');
}

console.log(createBoard(8));

Especially the last two changes are subject to personal preferences - some prefer the declarative style, some stick to if { ... } else { ... } everywhere - it's your (team's) choice.

There are several common 'tricks' that can reduce the perceived code complexity. Reduced nesting, fewer conditional branches and simpler conditions all improve code readability.

To improve code readability and reduce the perceived complexity, you need to reduce nesting, remove conditional branches, simplify if-conditions and switch to a more descriptive style. The following 'techniques' help to simplify your code sample: