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
I bought two stamps.
I bought two movie tickets.
テーブルの上にお皿が二枚ある。
There are two plates on the table.
二つ is the general-purpose counter for two items of any shape, while 二枚 specifically counts two thin, flat objects like paper or plates.
handsome man; good-looking guy · actor in a love scene; romantic lead
double-dealing; duplicity; speaking with a forked tongue
bivalve
carrying a palanquin as a pair; palanquin carried by two people
firmly planted stance; solid lower-body posture
Standard kanji spelling; the most common written form.
Numerical form used in lists, tables, or casual writing.
Compound of 二 (two) and the counter 枚 (for flat objects).
bivalves
ankle-kicking twist down
holding two positions at once (sumo)