Let's consider a directory with these files:
$ ls foo*
foo111.txt foo11.txt foo1.txt
Let's consider a minor variation on your script:
$ cat script
#!/bin/sh
echo No quotes $1
echo "Double quotes $1"
Now, let's run it:
$ bash script "foo*"
No quotes foo111.txt foo11.txt foo1.txt
Double quotes foo*
As you can see, the results are completely different. Without the double quotes, pathname expansion is performed.
To illustrate another difference:
$ bash script "long space"
No quotes long space
Double quotes long space
With double quotes, the long space between words is preserved. Without it, all contiguous whitespace is replaced with a single blank. This is an example of word splitting.