noun
two sheets; two flat objects
Counter for flat, thin objects such as paper, tickets, plates, CDs, etc. Used as a noun meaning 'two of such items'.
コピー用紙を二枚ください。
Please give me two sheets of copy paper.
映画のチケットを二枚買った。
I bought two movie tickets.
Means 'one sheet/flat object'. 二枚 is the two-item version of the same counter.
General counter for two items, not limited to flat objects. 二枚 is specific to thin, flat things.
Compound of 二 (two) and the counter 枚 (for flat objects).