Надо сделть так:
если $value="1", то галочка (checkbox) стоит, если $value="0", то не стоит.
Как это сделать?

$checked = ($value == "1") ?  "checked" : null;
echo '<input type="checkbox" '.$checked .'>';

<input type="checkbox" <?=($value==1) ? 'checked="checked" : null;'?>/>

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HTML, CSS (Bootstrap), JS(JQuery, ExtJS), PHP, MySQL, MSSql, Posgres, (TSql, BI OLAP, MDX), Mongo, Git, SVN, CodeIgnater, Symfony, Yii 2, JiRA, Redmine, Bitbucket, Composer, Rabbit MQ, Amazon (SQS, S3, Transcribe), Docker

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HTML, CSS (Bootstrap), JS(JQuery, ExtJS), PHP, MySQL, MSSql, Posgres, (TSql, BI OLAP, MDX), Mongo, Git, SVN, CodeIgnater, Symfony, Yii 2, JiRA, Redmine, Bitbucket, Composer, Rabbit MQ, Amazon (SQS, S3, Transcribe), Docker