Example sentences
tā他shì是wǒ我de的tóng同xué学。
He's my classmate.
tóng同xué学men们dōu都lái来le了。
The classmates all came.
About this word
同 means "same" and 学 means "study, learn". A 同学 is someone who studies the same thing in the same place, a classmate. The pattern is productive: 同事 (same work, colleague), 同行 (same trade), 同屋 (same room, roommate). One usage surprise for learners: 同学 is also a way to address a student you do not know. A stranger in the street may call out 同学! to get a young person's attention, roughly like "excuse me, young man".
The story behind the character
同
同 is a mouth 口 tucked under a cover 冂, with a line 一 drawn across it. Xu Shen explained it as 合會也, a gathering together. Picture people crowded under one roof, speaking with one voice. That is where 同 gets its sense of "same", and why 同学 is somebody who studies beside you.
学
The traditional 學 is a whole scene: 爻 (counting rods for divination) on top, two hands fiddling with them, and 子 (a child) below. A kid working the rods with his hands. That's the oldest picture of learning. Xu Shen wrote 学, 觉悟也: "to awaken."