In shell scripts, when do we use {} when expanding variables?
For example, I have seen the following:
var=10        # Declare variable
         
        Curly braces are always needed for accessing array elements and carrying out brace expansion.
It's good to be not over-cautious and use {} for shell variable expansion even when there is no scope for ambiguity.
For example:
dir=log
prog=foo
path=/var/${dir}/${prog}      # excessive use of {}, not needed since / can't be a part of a shell variable name
logfile=${path}/${prog}.log   # same as above, . can't be a part of a shell variable name
path_copy=${path}             # {} is totally unnecessary
archive=${logfile}_arch       # {} is needed since _ can be a part of shell variable name
So, it is better to write the three lines as:
path=/var/$dir/$prog
logfile=$path/$prog.log
path_copy=$path
which is definitely more readable.
Since a variable name can't start with a digit, shell doesn't need {} around numbered variables (like $1, $2 etc.) unless such expansion is followed by a digit.  That's too subtle and it does make to explicitly use {} in such contexts:
set app      # set $1 to app
fruit=$1le   # sets fruit to apple, but confusing
fruit=${1}le # sets fruit to apple, makes the intention clear
See: