Assurance is insurance against events that will inevitably occur.
The common example of assurance is life assurance.
There is often no real difference between assurance and insurance, for example with term life assurance (which only pays out in the event of death during the term of the assurance) although the long term over which life assurance is taken complicates all the actuarial calculations linked to it. This means that than insurance company's life business is harder to value, and has a less certain value, than its general business.
Some life assurance policies are a blend of insurance and savings. These are often complex making it difficult to value them, and returns are unlikely to be better than market rates for funds with a similar level of risk, however they can have tax advantages so may be worth considering for some investors. Note that in many countries the amount received by investors is tax free because tax has already been paid by the fund.