The term refers to the "cotyledon," or the embryonic leaves that first emerge from the seed before the "true leaves" grow. The true leaves are the leaves you typically see on a plant. They often look different from the cotyledons. As you might guess, a monocot has one cotyledon, and a dicot has two.
Most wildflowers you run into on the trail are dicots. When you discover that one is a monocot, you can instantly narrow down the options of what it might be. The following plant families are all monocots:
Tulips are in the Lily family, so they are monocots. Daffodils, in the Amaryllis family, are also monocots.
Within these plant families, it's often pretty easy to tell what's what. You can tell a grass from a palm, and a palm from a lily, right? Even if you can't, it helps you narrow down what you've got once you refer to a guidebook.
There are four traits to look for to tell monocots from dicots. Sometimes you can't see one but you can see another. Like, the plant may not be in bloom, but you can observe its leaves. Or you can see its flowers, even though you can't see its roots. Here they are:
One cotyledon for monocots, two for dicots. As noted above. Probably the least helpful bit of advice if you are trying to identify a flower, because the cotyledons will be long gone.
Dicots have tap roots, monocots don't. Have you ever tried to pull some grass out of the ground by the roots? (If not, give it a try.) There are tons of hairy roots on there, but no tap root. Or harvest an onion, and observe its hairy roots. There's no tap root. Then harvest a carrot. The carrot itself IS the taproot. Or perhaps you've tried to pull a dandelion out of the yard by the roots, and you've seen its enormous taproot. (By the way, every part of the dandelion is edible and very healthy, so if you do pull one out of the yard, look online and find out how you can eat it.) Carrots and dandelions are dicots. Grass and onions are monocots.
Leaves of monocots have parallel veins, leaves of dicots don't. Think of a blade of grass. The veins are parallel. Now think of a maple leaf (a dicot). The veins are most certainly not parallel. For this characteristic, as well as the previous two, if you can remember that grasses are monocots, then you can remember which traits apply to monocots and - conversely - which apply to dicots. Grasses have just one cotyledon (the blade of grass), no taproot, and parallel veins.
Monocots tend to have three or six petals and sepals, and dicots tend to have four or five. This last one is not a hard and fast rule, but it is common enough that you can often start by counting petals and then check the veins of the leaves for confirmation. It's good to do both because I have seen freak dicot flowers with six petals - a poppy and a strawberry plant. But generally speaking, if you count three or six petals or sepals, you're looking at a monocot.
Here are some photos as examples:
Crocuses. Six petals, and look at how grass-like the leaves are. Those look like blades of grass, but they are actually the leaves of the crocus.
Blue-Eyed Grass, in the Iris family. So grass-like that it was named for it.
Camas, in the Melanthiaceae family. Sorry I don't have a more familiar sounding name than the Latin for you.
Blue Dicks, in the Bromeliad family
NOT A MONOCOT. This Fire Poppy faked me out with it's six petals. This is a case where you want to check the plant's leaves to see the veins on them.
Mariposa Lily, on the John Muir Trail. Three petals.
Corn Lily, also on the JMT. These plants are named after corn, which is in the Grass family and also a monocot, because their foliage almost resembles a cornstalk.
Wild onion, in Lyell Canyon. An easy way to tell these guys from other monocots is that they smell oniony.
Mountain Pretty Faces, in the Asparagus family, on the PCT at Agnew Meadows
White Rein Orchid. This one is at Agnew Meadows on the short wildflower walk there, but I saw more at the campground at Red's Meadow.