Normally, annuities pay a pension until the annuitant dies (this type of annuity is specified by the name "life annuity"). Period certain annuities (also called "term certain annuities") pay a pension for a fixed period of time. If the annuitant dies before the pension period ends, the annuity will continue to pay its pension to whoever inherits the annuity from the original annuitant's estate.
Anyone can buy period certain annuities. The question of whether they are preferable to life annuities hangs on the question of what type of financial security the buyer prefers:
Life annuities promise an income stream for a lifetime. That's pretty good security because you know that your income will never stop while you need it. But buying a life annuity also carries an element of risk: what if you die early? You may not get a good return on your purchase because the pension may last for only a very short time.
With period certain annuities, on the other hand, your pension's duration is guaranteed. Whether you live another 6 months or another 100 years, you know exactly how long your pension will issue payments. The downside is that the pension might not last as long as you need income.
For a compromise between life annuities and period certain annuities, you might purchase a life annuity with a period certain option. A life annuity with a period certain option guarantees you at least a certain pension duration (specified in your contract), but if you outlive that period, it behaves like an ordinary life annuity.