What it means
From the blacksmith forge, where iron can only be shaped in the few moments it glows red hot. Let it cool and the hammer does nothing. To strike while the iron is hot is to act at exactly the right moment, while conditions are perfect and the chance is live, instead of dithering until the moment has passed and the heat is gone.
Usage examples
"The buyer is keen right now, so strike while the iron is hot and close the deal."
"They loved your pitch, so strike while the iron is hot and send the contract today."
"They loved the pitch, so strike while the iron is hot and send the contract today."
"She's in a good mood, ask her for the day off now and strike while the iron is hot."
"He's finally replied and sounds interested, so strike while the iron is hot and ask him out before the vibe goes floppy."
Where it comes from
It comes from blacksmithing. Hot iron can be shaped only while it's glowing and soft enough to hammer. Once it cools, that window shuts and the job gets harder or pointless. That's why the saying means move fast when the chance is ripe and alive, not after the moment's gone cold.