You're doing var assignment in wrong way.
var=$passvar|md5sum
You're supposed to send "$passvar" to md5sum. It won't go through pipe | by itself, so you either need to use echo, or printf. That will output things to stdout stream. You can capture that into variable with command substitution $(...). In other words, you should be doing:
var=$( echo "$passvar" | md5sum )
Also, please remember to quote the variables to preserve the integrity of data stored in them and prevent word splitting.
Other issues:
$ read -sp 'Your password:' passvar
Your password:$ var=$( echo "$passvar" | md5sum )
$ echo "$var"
2b00042f7481c7b056c4b410d28f33cf -
Notice two things here: there's no newline after "Your password", so you might want to add echo after that command. Second, notice that md5sum outputs filename after the calculated md5 checksum, which in this case is - or stdin stream. You might want to consider getting rid of that part via any text processing utility that will let you cut away words, like awk:
var=$( echo "$passvar" | md5sum | awk '{print $1}')
Alternatively, you can just make use of bash's read and here-string <<< (see this for more info on that operator) :
$ read var trash <<< $( echo "$passvar" | md5sum )
$ echo "$var"
2b00042f7481c7b056c4b410d28f33cf
Last but not least, your #! line is missing / before bin - it should be #!/bin/bash.
The complete script should be as so:
#!/bin/bash
read -p 'Your login: ' uservar
read -sp 'Your password: ' passvar
printf "\n"
read var trash <<< "$(printf "%s" "$passvar" | md5sum)"
printf "%s:%s" "$uservar" "$var" #> ~/results.txt
Note that I commented out redirection to file, just to see the output on the terminal for testing purpose. Here's how it works:
$ ./testing.sh
Your login: johndoe
Your password:
johndoe:912ec803b2ce49e4a541068d495ab570$
For future reference, you can add set -x after #!/bin/bash (given that you've properly defined the #! line, of course) to troubleshot the script and see what commands actually run and were errors might arise. Or just use shellcheck online tool.