You have two syntaxes to think about, PHP and SQL.
The SQL query you want will have single quotes in it.
SELECT dish, price FROM meals WHERE meal LIKE '%something%'
The PHP code is building a string by concatenating literal strings, enclosed in double quotes, with variables.
$string = "Some literal concatenated with a " . $variable . " plus another literal string";
Your literal string contains single quotes, so you will have single quotes within the double quoted literal.
$string = "A literal with 'single quotes' inside of it.";
The single quotes just happen to need to be before and after the variable you're concatenating with the strings, so you get the double quotes following the single quotes.
$string = "A string with a '" . $variable . "' enclosed in single quotes.";