Questions & Answers about qǐng jìzhù zhīfùmìmǎ.
Here, 请 means please. It makes the sentence polite.
So 请记住支付密码 is a polite instruction or reminder.
A useful extra note: 请 can also mean to invite or to treat someone, but not in this sentence. Here it is just a politeness marker.
Mandarin often leaves out the subject when it is obvious from context.
In an app, on a website, or in a notice, the hidden subject is usually 你. So this sentence is understood as:
请你记住支付密码。
The shorter version sounds very natural in instructions and interface text.
Yes, absolutely.
- 请记住支付密码。 = shorter, common in written instructions
- 请你记住支付密码。 = also correct, a little more explicit
Both are natural. In things like banking apps and warnings, the shorter form is especially common.