Yes, Tension is simply the force in the rope. Here is an example:
Consider the image above. I will explain how to solve using Tension. The general process is to consider the forces acting on each block, and then combine the equations.
1. Consider forces acting on the left block:
F_net = ma = UpForce - DownForce = Tension - mg (Here the rope is providing the upward force, so this is the tension force).
Therefore,
a = (T - mg)/m [where]
2. Consider forces acting on the right block:
F_net = Ma = UpForce - DownForce = Tension - Mg (Notice Tension is the same as in the previous example, this is a key feature of Tension.
Tension is always constant for the same rope. (if it wasn't the same, the rope would pull itself apart) Because this rope is the same as the rope attached to the left block, the tension in this rope is the same, so I cause the same variable T.)
Therefore,
a = (T - Mg)/M
3. Combine equations. Because as one side moves down, the other moves up at the same rate, the accelerations will be equal and opposite to each other.
Therefore,
(T - Mg)/M = (mg - T)/m
So,
m(T - Mg) = M(mg - T)
So,
mT - Mmg = Mmg - TM
So,
(m+M)T = 2Mmg
Therefore,
T = 2Mmg/(m+M)
Now that we know tension, we can calculate acceleration by simply substituting our answer here into one of the equations from either step 1 or step 2.
This process may seem tedious, but it is essential to know how to do this for more complicated problems that can be created.