I would like to know when and why should I use {$var}
echo \"This is a test using {$var}\";
and when (and why) should I use the simple form
The brackets allow you to remove ambiguity for the PHP parser in some special cases. In your case, they are equivalent.
But consider this one:
$foobar = 'hello';
$foo = 'foo';
echo "${$foo . 'bar'}"; // hello
Without the brackets, you will not get the expected result:
echo "$$foo . 'bar'"; // $foo . 'bar'
For clarity purposes, I would however strongly advise against this syntax.