Is there an easier/analogous explanation of geometric mean, similar to that of arithmetic mean? My simple understanding of arithmetic mean is that the arithmetic mean represents a "central point" (central tendency) where all others numbers converge as the accumulative linear distance from the left equals the accumulative linear distance from the right.
While I know (memorize) the definition of geometric mean, I cannot "interpret/visualize" it (maybe I should not?) in a way analogous to that of the arithmetic mean. I suspect that it may have to do with the fundamental concept of "root", which I fail to grasp, (I did try to read up on the concept of root but have yet found anything beyond its definition and application) but still I cannot find a satisfying answer how taking an nth root would yield a "mean" that reasonably represents the group.
Is there an easier way to "understand" geometric mean? (I tried to look for a similar question in this forum but have not found one so far).

I think of the geometric mean as a log-scale version of the arithmetic mean. That requires a little explanation.
The arithmetic mean of $x_1, \ldots, x_n$ is $\mathrm{AM}(x) = \frac{x_1 + \cdots + x_n}{n}$. Set $y_i = b^{x_i}$ for a fixed base $b>1$. Then the geometric mean of $y_1, \ldots, y_n$ is
\begin{align*}
\mathrm{GM}(y) &= (y_1 \cdots y_n)^{1/n} = (b^{x_1 + \cdots + x_n})^{1/n} = b^\left(\frac{x_1 + \cdots + x_n}{n}\right) \\
&= b^{\mathrm{AM}(x)}.
\end{align*}
As an example, suppose we had 3 bank accounts with $y=\$100, \$1000, \$10000$ in them. The arithmetic mean is basically only going to pick up the \$10000 amount and will be basically $\mathrm{AM}(y) \approx \$10000/3$. However, the geometric mean effectively thinks of these as $\$10^2, \$10^3, \$10^4$ where $x=2, 3, 4$ with $\mathrm{AM}(x) = 3$, so the geometric mean of the amounts in the bank is $\mathrm{GM}(y) = \$10^3 = \$1000$.
Lots of data is really of the form $b^x$. For instance, this is basically the insight behind Benford's law. Consequently the geometric mean is sometimes more appropriate than the arithmetic mean.
