By one dimension we mean that the body is moving only in one plane and in a straight line.
Like if we roll a marble on a flat table, and if we roll it in a
straight line (not easy!), then it would be undergoing one-dimensional
motion.
There are four variables which put together in an equation can describe this motion. These are Initial Velocity (u); Final Velocity (v), Acceleration (a), Distance Traveled (s) and Time elapsed (t). The equations which tell us the relationship between these variables are as given below.
v = u + at
v2 = u2 + 2as
s = ut + 1/2 at2
average velocity = (v + u)/2
Armed with these equations you can do wonderful things like calculating a cars acceleration from zero to whatever in 60 seconds !!