You say it like the number eight. It’s a small island, especially in the River Thames.
Anyone living along the Thames upstream of London as far as about Windsor or Reading will know this word, as it often appears in the names of the little islands that dot the river in those reaches. But for most British people it surfaces only as a curious term during commentaries on the Oxford-Cambridge boat race, when places such as Chiswick Eyot are regularly mentioned.
It’s from Old English iggath (or igeth), which is based on ieg, an island, plus a diminutive suffix. So it means a small island. As you might expect from its Old English credentials, it turns up in J R R Tolkien’s Lord of the Rings: “That night they camped on a small eyot close to the western bank”.
An older form that’s more obviously connected to the way that you say it is ait, a spelling retained in the names of some of the Thames islands.
Upon this ait a house of entertainment has been erected; and here the river steamers are accustomed to land great numbers of holiday folks, desirous of the delights of pure air, and solicitous to banquet upon eel-pies, for which the tavern is famed.
A Picturesque Tour of the River Thames in its Western Course, by John Fisher Murray, 1849.