text bubble with dots after you send a text

It means someone on the other end is typing.

It means the recipient has Messages open and their keyboard is active, even if they’re not actually typing a response, although it’s very likely that’s what they’re doing.

quailway wrote:

Typing a reply to my text, or sending a text to another person?

If you never see a response, they were probably replying to someone else. However, I have, on more than one occasion, typed a reply to someone and forgot to press send. Or, had to go do something else. Or changed my mind.

Short answer: there is no real way to know.

It can also mean they are responding to someone else.