Why is there an unexplainable gap between these inline-block div elements?

In this instance, your div elements have been changed from block level elements to inline elements. A typical characteristic of inline elements is that they respect the whitespace in the markup. This explains why a gap of space is generated between the elements. (example)

There are a few solutions that can be used to solve this.

Method 1 - Remove the whitespace from the markup

Example 1 - Comment the whitespace out: (example)

<div>text</div><!--
--><div>text</div><!--
--><div>text</div><!--
--><div>text</div><!--
--><div>text</div>

Example 2 - Remove the line breaks: (example)

<div>text</div><div>text</div><div>text</div><div>text</div><div>text</div>

Example 3 - Close part of the tag on the next line (example)

<div>text</div
><div>text</div
><div>text</div
><div>text</div
><div>text</div>

Example 4 - Close the entire tag on the next line: (example)

<div>text
</div><div>text
</div><div>text
</div><div>text
</div><div>text
</div>

Method 2 - Reset the font-size

Since the whitespace between the inline elements is determined by the font-size, you could simply reset the font-size to 0, and thus remove the space between the elements.

Just set font-size: 0 on the parent elements, and then declare a new font-size for the children elements. This works, as demonstrated here (example)

#parent {
    font-size: 0;
}

#child {
    font-size: 16px;
}

This method works pretty well, as it doesn't require a change in the markup; however, it doesn't work if the child element's font-size is declared using em units. I would therefore recommend removing the whitespace from the markup, or alternatively floating the elements and thus avoiding the space generated by inline elements.

Method 3 - Set the parent element to display: flex

In some cases, you can also set the display of the parent element to flex. (example)

This effectively removes the spaces between the elements in supported browsers. Don't forget to add appropriate vendor prefixes for additional support.

.parent {
    display: flex;
}
.parent > div {
    display: inline-block;
    padding: 1em;
    border: 2px solid #f00;
}

.parent {
    display: flex;
}
.parent > div {
    display: inline-block;
    padding: 1em;
    border: 2px solid #f00;
}

<div class="parent">
    <div>text</div>
    <div>text</div>
    <div>text</div>
    <div>text</div>
    <div>text</div>
</div>

Sides notes:

It is incredibly unreliable to use negative margins to remove the space between inline elements. Please don't use negative margins if there are other, more optimal, solutions.

Using inline-block allows for white-space in your HTML, This usually equates to .25em (or 4px).

You can either comment out the white-space or, a more commons solution, is to set the parent's font-size to 0 and the reset it back to the required size on the inline-block elements.

Found a solution not involving Flex, because Flex doesn't work in older Browsers. Example:

.container {
    display:block;
    position:relative;
    height:150px;
    width:1024px;
    margin:0 auto;
    padding:0px;
    border:0px;
    background:#ececec;
    margin-bottom:10px;
    text-align:justify;
    box-sizing:border-box;
    white-space:nowrap;
    font-size:0pt;
    letter-spacing:-1em;
}

.cols {
    display:inline-block;
    position:relative;
    width:32%;
    height:100%;
    margin:0 auto;
    margin-right:2%;
    border:0px;
    background:lightgreen;  
    box-sizing:border-box;
    padding:10px;
    font-size:10pt;
    letter-spacing:normal;
}

.cols:last-child {
    margin-right:0;
}

Any easy fix although it's a bit outdated at this point in time is to just float the container. (eg. float: left;) On another note, each id should be unique, meaning you can't use the same id twice in the same HTML document. You should use a class instead, where you can use that same class for multiple elements.

.container {
    position: relative;
    background: rgb(255, 100, 0);
    margin: 0;
    width: 40%;
    height: 100px;
    float: left;
}