From looking at your source code, it seems that you have wrapped content, such as your images in HTML heading tags <h4> ( as kjodle) mentions. You should use the Text editor view for your posts and remove unnecessary code.
For example: Your most recent post in Events has a H4 heading wrapping the image and the text following. Instead it should look like this in the Text editor view:
Your code looks like:
<h4>
<a href="https://chamberswild.com/wp-content/uploads/2011/09/RailWalk_ANWR.jpg">
<img class="size-medium wp-image-3320 alignleft" width="300" height="180" src="https://chamberswild.com/wp-content/uploads/2011/09/RailWalk_ANWR-300x180.jpg" alt="RailWalk_ANWR">
</a>
</h4>
<h4></h4>
<h4>Take one of the annual Rail Walks through the marshes of Anahuac NWR, sponsored by FOAR. Free and open to the public, no reservations needed. See their site for more info and visit right away!
<strong> </strong>
</h4>
<p> </p>
But a change to this will allow the image float to work:
<a href="https://chamberswild.com/wp-content/uploads/2011/09/RailWalk_ANWR.jpg">
<img class="size-medium wp-image-3320 alignleft" width="300" height="180" alt="RailWalk_ANWR" src="https://chamberswild.com/wp-content/uploads/2011/09/RailWalk_ANWR-300x180.jpg">
</a>
p>
Take one of the annual Rail Walks through the marshes of Anahuac NWR, sponsored by FOAR. Free and open to the public, no reservations needed. See their site for more info and visit right away!
</p>