Unfortunately there is no default way to resize columns in Kanban boards. We do have an improvement request for that under https://jira.atlassian.com/browse/GHS-9236, you can add yourself as a Watcher to get notified on that along the time.
Also, a possible workaround for this would be creating a bookmark in your browser with the following bookmarklet as text:
This sets the width of the left pane to 500px when you run the bookmarklet.
To expand on Jose's answer here's a longer bookmarklet that's a bit more convenient to use.
It keeps the standard size as the minSize and you can set the maxSize to however wide you'd like and then it steps between them using incrementBy.
Atlassian Update – 29 January 2019
I'm happy to announce that this feature is coming to you shortly with Jira 8.1, together with a larger set of improvements for Jira boards. If you have any questions or feedback, feel free to reach out to us in the comments.
Jira Server Team
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