A fertility monitor is a device designed to analyze some changes that take place during a woman's menstrual cycle in order to know with great accuracy when an ovulation is going to occur, to have the best chances of getting pregnant. See more on how to get pregnant.
They are similar to ovulation tests, that tell you the 2/4 most fertile days, depending on the type, while monitors tell you up to 6 most fertile days.
Most of them are intended for women who want to get pregnant; one, as far as I know, is for contraception purposes but I think it can be used in both ways.
I'll explain here in simple words how they work, without going into many scientific details.
A fertility or ovulation monitor follows a woman's cycle, suggesting on which days there is a possibility of falling pregnant. It does this by measuring the levels of two hormones in the woman's urine during her cycle. A fertility monitor is more accurate than ovulation tests that only use sticks.
There is a monitor and test sticks: every month, on certain days it will ask you to do a test. When the levels of certain hormones raise, it means you are about to ovulate so you will know that those are your most fertile days. Those are the best days to conceive your baby.
The monitor keeps the information about your cycles for several monts, so every month it will ask you to take a test on specific days, which may vary form month to month.
A woman is most fertile around the middle of her cycle, when an egg is released (ovulation). So it is correct that you should know when these days are but there are also more days when there is a danger, or the opportunity, of falling pregnant. Let's see why.
Let's say you have an ideal 28 day cycle, so your most fertile days should be between the 13th and 15th. However, sperm can survive inside a woman's body for up to five or six days, so if you have an intercourse on the 11th or 12th day, your egg may not yet be mature but sperm stays within you and within one day or two may meet and fertilize the egg. Also the egg may be fertile up to a couple of days after the ovulation occurs.
So, for the best chances of getting pregnant you should have intercourses from a few days before the ovulation is supposed to occur to a couple of days after the ovulation.
The monitor can help you spot those days.
There are different types of monitors with different characteristics. Read descriptions of them.