What exactly means 'delta' in gradient descent algorithm?

I am not completly authorized to answer this question but maybe it will be helpful if i say that this term is derivative of the theta, which is used to control aspects of cost function minimization (direction and rate). Let theta be a coordinate on X-axis (name it A) . B will  be corresponding coordinate on Y-axis. If  You draw tangent line to function J at point (A, B) the deriviative will be the slope of this tangent line.

It's just a derivative.