EOI in life insurance stands for "evidence of insurability". When you are taking an exam to get a life insurance, you are providing evidence of insurability. It is whatever is required to show that you are qualified to obtain that policy.
When life insurance does not require EOI, that can make the policy very expensive, as in guaranteed issue life insurance, which has no evidence of insurability requirements.
However, sometimes no EOI can be a perk. E.g Many term policies offer the opportunity to convert them to permanent policies without evidence of insurability. That is a perk, especially if your health deteriorates and you cannot qualify for a new term policy. It is a double perk in that the converted permanent policy will be rated the same as your term policy was.
When life insurance does not require EOI, that can make the policy very expensive, as in guaranteed issue life insurance, which has no evidence of insurability requirements.
However, sometimes no EOI can be a perk. E.g Many term policies offer the opportunity to convert them to permanent policies without evidence of insurability. That is a perk, especially if your health deteriorates and you cannot qualify for a new term policy. It is a double perk in that the converted permanent policy will be rated the same as your term policy was.