Electric field strength is a measure of the electric stress set up in an insulator. If a sufficiently high potential difference is applied across an insulator, electrons can be teared from the atom nuclei and causes the flow of current. This is known as insulator breakdown. To avoid the breakdown, all insulating materials are rated according to the maximum voltage that may be safely applied. Electric field strength is then equal to V/d assuming the uniform distribution of the charges which generate the constant electric field over the distance d.
Electric field is very strong when a huge potential difference across a unit distance.
Electric field is also very strong when a unit potential difference across a very tiny distance.