Question: I am currently studying Graph Theory and want to know the difference in between Path , Cycle and Circuit. 

I know the difference between Path and the cycle but What is the Circuit actually mean.

Answer: 
I think I disagree with Kelvin Soh a bit, in that he seems to allow a path to repeat the same vertex, and I think this is not a common definition. I would say:

Path: Distinct vertices $v\_1,\dots,v\_k$ with edges between $v\_i$ and $v\_{i+1}$, $1 \le i \le k-1$.

Trail: A sequence of not necessarily distinct vertices $v\_1,\dots,v\_k$ and a sequence of edges $e\_1,\dots,e\_{k-1}$ such that $e\_i$ connects $v\_i$ and $v\_{i+1}$, $1 \le i \le k-1$ and all of the $e\_i$ are distinct.

Cycle: Distinct vertices $v\_1,\dots, v\_k$ with edges between $v\_i$ and $v\_{i+1}$, $1 \le i \le k-1$, and the edge $\{v\_1,v\_k\}$.

Circuit: A trail with the same first and last vertex.

Note: In some old texts the word circuit is sometimes used to mean cycle.
cycle is a closed path with no vertices repeated.