Is it only the math or the physics/physical concepts that you don't get?
In this problem, you have a constant pressure of 1.00 atm. This being the case, it is an isobaric system (constant pressure), and so you have the equation that work (W) = -pressure(P) x change in volume (∆V)
This is written as W = -P∆V and is known as pressure-volume work.
Now, understand the conventions that are used.
-If work is done ON the system, it has a positive sign (+)
-If work is done BY the system, it has a negative sign (-)
In this problem, the gas is being compressed, i.e. the volume decreases, and so work is being done ON the system. Thus, the sign of W is positive (+). This comes out automatically because of negative sign in front of P∆V,
So, we have W = -P∆V and substituting values, we have
W = -(1.00 atm)(1.5L - 1.25L) = -(1.00 atm)(0.25L) = -0.25 L-atm
Converting this to joules, we get -0.25 L-atm x 101.3 J/L-atm = -25.3 J (note the negative sign)
Hope this all helps a little.