Today I had attended my introductory course of topology, and the lecturer used the term "continuous deformation" without proposing its formulated definition.
Had looked up wikipedia, it generally shows the concept of homeomorphism, not with exact terminology "continuous deformation"
I roughly guess the concept/definition of topology is with which to make a opens sets upon a given set so that we can generalize our understanding of continuity.
To define continuity of function, one generally needs to define the right-next element in domain set, so the concept of topology helps it to be realized I guess.
Is there any further reading, recommendation or intuitive explanation to understand the term "continuous deformation" clearly?
I believe that the lecturer was referring to homotopy. A homotopy between two continuous functions $f,g: X \to Y$ is a continuous function $$H : X \times [0,1] \to Y$$ such that $H(x,0)=f(x)$ and $H(x,1)=g(x)$. It was probably referred to as a continuous deformation because it was looking at the image of $f$ and $g$. For example, if $f$ and $g$ are paths in your space, then $H$ will describe a continuous deformation of the image of the first path to the image of the second one.