Demetrius is called fickle because his romantic interests change easily. We are told that he was once in love with Helena, but when she introduced him to her friend Hermia, he fell out of love:

For ere Demetrius look'd on Hermia's eyne,
He hail'd down oaths that he was only mine;
And when this hail some heat from Hermia felt,
So he dissolved, and showers of oaths did melt. (1.1)

Essentially, Demetrius claimed that he would love Helena forever, but as soon as he saw Hermia, he abandoned Helena and began to pursue her friend.

It is also worth noting that Hermia is the daughter of Egeus, who appears to be close to Theseus. We don't ever meet Helena's parents and are told only that she is "old Nedar's Helena" (1.1.116). We don't ever find out who exactly Nedar is, but he is obviously not as prominent in the Athenian court as Egeus, so perhaps Demetrius was motivated by Hermia's wealth and position at court as well as her looks.

Demetrius is fickle because he breaks his promises as soon as something "better" comes along.