And && is logical AND.
Typically, || and && are used in if-statements, to combine multiple conditions.
A quick example:
nrSongs=`ls -1 *.[Mm][Pp]3 | wc -l`;
#the above statement executes the "ls" command, passes it's output to "wc" utility for counting the lines
#and stores the result (number of lines) in the variable $nrSongs
if (( $nrSongs > 0 )) && (( $mySum < 11 )); then
echo "There are between 1 and 10 songs in the current directory `pwd`.";
`` are called backticks. They run a command and capture it's output, for instance for substitution into a string or command (like in amdGIntel's post) or for saving it into a variable (like in example above).
Please distinguish them clearly from '' (single quotes) and "" (double quotes), which all have distinct meanings to the shell.
For more info, read up on quoting, pipes, IO redirection and stuff like that in "man bash" (or the man page of your shell, if you're not using bash).