1. wait for a short time, wait a while
hold/hang on a minute/second/moment while I do sth
If you ask someone to 'hold on' or 'hang on', you are asking them to wait for a short time. You might use this expression while leaving a call for a moment or before putting someone on hold. In everyday spoken English we might shorten this to 'just a sec', or use 'give me/gimme a second/minute/moment' instead of hold/hang on. You can use it to ask for time to find something or someone: "Do you have that photocopying done for me? - Yes, it's here somewhere. Hold on a second." Despite this expression sounding very casual, you will hear it in business contexts a lot.