Tightening your diaphragm?

People have told me to do this when I sing but I do not really get what they mean...

Can someone help explain this to me?

okay, the first few answerers have given you the ground level meaning.It's a bit more thorough than that:
when we go to inhale for everyday breathing, the diaphragm does its one-and-only move, it contracts and flattens out a bit. This leaves a change in air pressure in our bodies, the lower ribs expand, the air rushes in, and the air pressure becomes balanced again. Then the muscles of exhalation ( which does not include the diaphragm, snce it has become passive at this stage) bring the diaphragm back up to its original position, the air leaves the body, the ribs contract, etc. We have exhaled. Then there's a tiny break for recovery, and the whole cycle starts again.
For singing, we want to fill the lungs to the best of our ability. ( Mostly, we take little shallow breaths that fill only the top third of our lungs) We want to feel not only our bellies expanding, but also our flanks ( at the side) and our backs. We feel all this gear moving when we laugh a hearty laugh ( the ho-ho-ho type comes to mind this time of year). these are the muscles that we want to engage for singing. The trick behind a good singer's breath control or breath management is knowing how to slow down the rate of exhalation. Singers often talk about the "gesture of inhalation". When you have tanked up good and proper, using all those belly/flank/back muscles, you will feel sturdy and balanced in your body. Trying to maintain this "full" feeling is what comes next. You will feel a gradual intensity /tightening/ expansion around the middle ( the diaphragm does not tighten any more at this point, it has reached its lowest point by inhaling) and you keep it going for as long as your air supply lasts. Then you let the muscles recoil very quickly, in order to relax enough for the next in-breath ( which ideally should not make any rasping asthmatic noise in your throat).
Sometimes asking your chorus director is not enough.Sometimes you need to seek out a singing teacher who can show you, hands-on, how to do this.

It's very simple.
You have a diaphragm, and you tighten it when you sing

It's a feeling you should get when you sing out strongly. When you breathe in and out, the part of your stomach that goes in and out is your diaphragm. When you tighten it, it's like flexxing when you wanna see your muscles. The muscles in your diaphragm will "flex". It's like flexxing your abs. ^_^

People use this phrase in reference to breathing. When you sing, taking in a deep breath can really help your tone. When you breathe, your shoulders should not come up at all. Rather, your stomach should come out. That way, you have a lot more air and will be able to sing through your phrases without taking a breath in the middle. To tighten your diaphragm is to push out the very last bit of air in your lungs to get through a phrase, and also to have a steady tone. The more air you use when you sing, the more open and strong your voice will sound. Another great tip is to open the back of your throat like you do when you yawn. This really helps your tone and aids in getting out high notes.

When you breathe, you breathe from your lungs, right? Inhale deeply. Feel your lungs and shoulders raise. Your stomach will go in and you will be able to feel your ribcage easier. That is NOT breathing from your diaphragm. When you learn how to breathe from your diaphragm in order to sing from it. Inhale. Make your stomach go out, instead of in. Fill up your lungs with air. Now, slowly exhale. Feel how your stomach is now going in as you continue to exhale. This IS breathing from your diaphragm. Keep practicing, and eventually while singing, it will become a habit and you will be singing from your diaphragm! Good luck! Hope I helped!