The Roman historian Tacitus in his book Germania mentions a Aesti or Aestii people. After Tacitus, Aestis speak language related to British, worship a 'mother of the gods' and wild boar, use clubs and sometimes iron weapons. They are also the only people to gather and trade amber.
Most of scholars identify those people as ancient Prussians speaking Baltic language closely related to modern Latvian and Lithuanian.
This identification is based mainly on their association with amber, a luxury item from Roman time with known sources at the southeastern coast of the Baltic Sea.
Some historians think Aesti may refer to all peoples living at Eastern coast of Baltic Sea, including Estonians speaking language of Finnic group.
Tacitus mentions Fenni people (probably Sami) living next to Aesti, which matches Estonians better than Prussians.
Whatever the case, it seems the word was eventually applied specifically to Estonians and is the origin of the county name of Estonia, called Eistland in ancient Scandinavian Sagas and Estia, Hestia and Estonia in early Latin sources.