It has been my experience that most young singers don't have a clue what support is. Why should they? For them, it functions unconsciously, or not all. As you get older, if you want to keep singing, it becomes crucially important to figure out what this support thing is all about.
Most of us, as students, have received critiques from teachers that say "not enough support for the upper register". This is all well and good; but what, exactly, are we supposed to do? Clench our derrière, as one beloved Canadian coach famously advised? Try harder? Push down and out like giving birth (ouch)?
I can tell you from experience, that without support, your high notes still won't work, even if you know how to open in the upper register. My favorite equivalent term for support is "body response". I like this because it implies that support is more something that has to happen, rather than something you muscularly inflict on yourself. Fine, but what exactly is it?
The upper register requires more compression from the abdominal system than the rest of the voice. This compression aids vocal fold closure. Remember that high notes require a high degree of tension in the vocal folds and high sub-glottal pressure. By using the abdominal system to generate sub-glottal pressure, we don't have to use pressure at the vocal fold level. The easiest way to feel this resistance in the body is to blow up a balloon (thanks to Ingo Titze) or sustain an "f" sound (fricative) with plenty of energy, This leaves your hands free to explore. They will show you exactly how the compressive function of the abdominals is expressed in the body.
Once you have a clear feeling for what is supposed to happen in the muscles below the nipple line, check in with the abdominal area while you sing the high note. If you are doing the rest correctly (lightness, placement, opening, vowel modification if necessary), it will give that last bit of "oomph" you need to sustain the tone. Oh, and don't forget, keep the ribs out in the onset. It will get the tone started the right way.