Another aspect to this - and one that can help with understanding and remembering the names - is to actually look up the names and break them down.

Take common basin sagebrush for example: Artemisia tridentata

Artemesia - from the Greek goddess Artemis (apparently Wormwood [family? in this case] was sacred to her?).

Tridentata - tri=3, dent=tooth. Look at the 3-toothed leaves and it makes good sense. Think tricycle (three wheels) and dentist as cognates.

Words, even Latin words, have meaning and there's (usually) a good reason for plants to have the names that they do. Exploring the etymology can (and probably should) be done for everything you're trying to commit to memory. And it's a fun exercise in its own right. It's an awfully lot like playing with conceptual (linguistic) legos.

Breaking down the word not only helps with understanding the plant in question, but also with other plants, as you start to recognize those words. Example: angustifolius = narrow leaf, folia, folius folium all mean leaf. So when you see names like absinthifolius,
acaciifolia, and acanthifolium, you already have a head start in understanding the meaning.

Very good points in the article and the above posts!

Indeed! Some of the names also indicate color of the plants/flower - alba = white, rubra = red, flavus = yellow, caeruleus = blue.

Yep, although some also reflect the names of the botanists who 'discovered' and documented them. Orchids are bad for this and are now in a huge upheaval of name-changing.

How about Habenaria erichmichaelii? You'd think Mr. Erich Michael might have been satisfied with just putting his last name on it, wouldn't you?

A little caveat on this, although I do like to know the Latin names too - some people think you are being a snobby elitist if you spout Latin names too much. I volunteer at Plant Clinics where it's encouraged to use common names with the general public unless you're asked specifically for a botanical name.

Mostly I like to see the blank look on faces when a neighbor says, "Oh, what is that pretty flower?" and I hit them with the botanical name - saying it as rapidly as possible.
I wait a beat or two and then lighten up to give them not only the common name, but will tell them if the plant is edible or medicinal.
Almost every time they will go home with at least one plant that they had admired.