In mechanism of electricity in conductors my teacher said the free electrons collide with positive lattice and this positive lattice is oscillating about its mean position. Ok for producing current battery is used. Now my question is why this positive lattice oscillate about a mean position and why it cannot move freely like electrons and if it is positively charged why it cannot go to negative terminal of the battery .my teacher also said that free electrons undergo zig zag motion after colliding and my question is why?
This is a very good question, and one that is very hard to give a good complete answer. The answer is the entire field of solid state physics.
It's a bit of luck, or a mystery, as to why we can understand it at all. Nature has arranged things so that the positive charges are firmly held in place by chemical bonds, which of course, comprise electrons. But in some materials (metals, for example), the "outermost" electrons are not so involved in bonding, and move through the solid almost as if there were no positive charges at all. Almost. Electric fields accelerate the charges as if they were free. But of course, if the electrons were completely free, they would accelerate without bound in the presence of the field.
The electrons are not completely free. In an ideal crystal, they would act as if they were completely free. But no solid is perfect. For one, there are always impurities. The accelerating electrons hit them, and can be imagined to stop, and start from zero velocity again, accelerating until it hits the next impurity. In consequence, the electron has a steady average velocity, a velocity that does not increase without bound. That's a very crude model, but it does a surprisingly good job of helping to understand what's going on.
For another, the crystal has defects. A defect is a kind of impurity, and similarly interferes with the progress of the electron.
And finally, when a positive ion vibrates, it moves from it's ideal equilibrium position. This, too, is a "defect" of sorts, and can "stop" (or deflect) the electron.
So we have a picture or metaphor (and it's just that ... a picture or metaphor not to be taken too seriously) of electrons stopping and starting, and zig-zagging through the metal.