Translation is when we move an object in an $n$-dimensional space, to another point in the same space. It can be used to remove the mean of data points from a dataset. Mathematically we can define by a transformation matrix equation as follows:
If we have a dataset $\mathbf{A}$, with $m$ rows (instances), and $n$ columns (features), then we mean centre it:
$$ \mathbf{A}_{mc}= \begin{bmatrix} \mathbf{A} & \mathbf{1} \end{bmatrix} \mathbf{W}_{mc}. $$ The translation matrix is $$ \begin{bmatrix} 1 & 0 & \dotsb & \dotsb & 0 \\ 0 & 1 & \dotsb & \dotsb & 0 \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ - \mu_1 & - \mu_2 & \dotsb & \dotsb & 1 \\ \end{bmatrix} $$
So now is it an orthogonal transformation or not ? I think, it is not an orthognoal transformation since the translation matrix is not orthogonal, but I am not sure, could some one clarify this ?
By definition, an orthogonal transformation of $A$ is multiplication of $A$ by an orthogonal matrix, and nothing else. You have (cleverly) included an additive term alongside $A$. That disqualifies the map from being orthogonal.
Translation is an isometry of Euclidean space (see: Euclidean group). These are precisely the maps of the form $x\mapsto Mx+b$ where $M$ is an orthogonal matrix and $b$ is any vector. Translation is a special isometry, with $M$ being the identity map.