Conditional convergence is fragile,
in the sense that the terms of
a conditionally convergent series can be rearranged to make the series
converge to any value, or can make
the series diverge. This fact is called
the Riemann
Series Theorem, which you might want to research
further. It is very strange and wonderful.
In contrast, absolute convergence is
robust, in the sense that rearranging the terms
of an absolutely convergent series does not change its
value. It behaves more like a finite sum.
The following video explains these ideas, and in particular looks at
an example of a conditionally convergent series, and gives the
arguments showing that after rearranging its terms, it converges to
different values, and even diverges.