Were you out last night to see the Moon and Mars together? It was a lovely get-together! I took some pictures, and here's the best one:
Mars is the reddish "star" to the left of the Moon. A couple of actual stars are visible as well, and the pink blob on the left is a reflection of the Moon inside the camera.
Funny, you can barely see Mars in the picture, but it was really obvious by eye. That's because cameras see things linearly -- an object twice as luminous as another will appear twice as bright in a picture -- while our eyes see things logarithmically -- a mathematical function that lets our eyes see a much larger range of brightness based on multiplication, not addition. It's actually a bit more complicated than this, but the point is while to the camera the Moon was vastly brighter than Mars (about 30,000x as bright!), to my eye the difference wasn't nearly as much (only about 10x as bright). This allows our eye to detect faint and bright objects at the same time, which a camera can't do easily.
You may have read that the Moon looked so bright last night because it was at perigee, the point in its orbit when it's closest to Earth. Honestly, that makes no difference to the casual observer. While it really was a bit bigger and brighter, the difference over a normal full Moon is pretty small, and you don't have anything to compare it with. If you could have superimposed a normal full Moon next to the Moon last night you might have seen a difference, but with just the one Moon sitting there you'd never notice.
This reminds me of the time in 1999 when people said the perigee full Moon would be so bright you could drive at night without headlights! Yeah. Bad idea.
But I do hope that some of the hype got people outside and noticing the sky. It's amazing what you can see, what lovely things await you, if you simply look up.