In this epic poem, the Achaeans are the people that we tend to think of as "the Greeks." These are the people who have come over from what is now Greece to fight in Asia Minor (what is now Turkey) against the Trojans. To modern archaeologists and historians, the term "Achaeans" is connected to a civilization that is known as the Mycenaean civilization.
As far as individuals go, the Achaeans were people like Achilles and Agamemnon and Patroclos.
There are also points in the Iliad where the Greeks are called by different names. They are also known as the Danaans and as the Argives. These are the same people as the Achaeans.