How to get a variable value if variable name is stored as string?

You can use ${!a}:

var1="this is the real value"
a="var1"
echo "${!a}" # outputs 'this is the real value'

This is an example of indirect parameter expansion:

The basic form of parameter expansion is ${parameter}. The value of
parameter is substituted.

If the first character of parameter is an exclamation point (!), it
introduces a level of variable indirection. Bash uses the value of the
variable formed from the rest of parameter as the name of the
variable; this variable is then expanded and that value is used in the
rest of the substitution, rather than the value of parameter itself.