in the lagrangian description or approch you follow each particle of the fluid individually as if you place a detector on each one of them and register position velocity and acceleration in each time in this case thes quantities depend only on time ie x(t) v(t),a(t)
in the Eulerian description you place a detector in each point in the fluid and fix it there and as the particles pass by you register the previous quantities, of course the position is known only velocity and acceleration need to be measured in this case v=v(x,t) and a=a(x,t) you see that in the eulerian approch we take a photography of the whole fluid motion in each instant of time which a much more useful picture than a bunch of intersecting pathline for each particle this is not to say that the Lagrangian approch is not useful its is and in some situation the only valid one but in the general case the Eulerian one is prefered
i hope add something to your understanding