An expression is code that primarily acts to return a value. This
largely corresponds to the concept of an rvalue used in
some languages, where an expression is logic evaluated within the code
(stack) but which does not inherently have an address that could be
referenced (though the result could be assigned or the expression could
be the body of a subroutine.
In my opinion, languages tend to fall along a spectrum where some are more expression-oriented in that arbitrarily complex logic can be assigned using expressions which may lead to dense code but also avoids what may be unnecessary assignments (which can be distracting), whereas others tend to be more statement-oriented in that logic is more likely to be broken across different statements regardless of whether there is a logical motivation to do so. Drawing on some of the oldest languages, Lisp and C lean towards each end respectively.
I personally have a penchant for functional programming practices which draws me toward more expression-oriented practices, though I also work to stay within the idioms of the language used.
Bash does not provide a means for typical generalized expressions,
but the use of subshell expansion can deliver many of the same benefits
using the form $(<body>) (backticks are also an older
option but the indicated format is preferred).