According to the Merriam-Webster Collegiate Dictionary, Eureka! is:
1) the exclamation that Archimedes used "on discovering a method for determining the purity of gold," or
2) an adjective that means "marked by sudden triumphant discovery." 
It is true; we are on a journey of priceless discovery, so either definition would fit. The bits of understanding gained in those Eureka moments are like nuggets of gold to be treasured forever. Though very basic, the following breakthrough concepts are shared by many of us:
Annual Flower Seeds
As a child, I once placed some flower seeds in a foam cup filled with dirt. Watering it faithfully, I was happy to notice little sprouts appear. The seedlings were supposed to become beautiful flowers, and in my childish wisdom, I believed the cup was all that was necessary. But when the crowded, stunted flowers failed to resemble those pictured on the front of the flower packet, I lost hope in my foam cup garden.
Over the years, my knowledge of growing flowers remained limited to information on packs of annual flower seeds from the store. I no longer completely trusted the pictures on the front, but the tidbits of information found on the back of those seed packs caught my eye.
Have you seen the date that says, "Packed for 2009" or "Packed for 2010" (fill in the year—any year—on a seed packet)? As a newbie, I understood it t mean if I failed to plant the seeds when the package said so, those flower seeds would expire. Consequently, I threw out many seeds in much the same manner as a homemaker throws out expired milk or eggs, without considering the remaining usefulness of the product.
Now that I am older and wiser, I keep all the seed packets I acquire; it's quite a collection. If some germination potential has likely been lost due to storage time, I sow double or triple the amount. But I never throw seeds away. Even though dates are useful for knowing when the seeds were gathered (due to a general decline in viability over time), dates generate business for seed companies. As a result, some shoppers throw out their year-old-seeds and flood the stores each spring to buy new ones.
So, not only do I keep commercial seed packets and find viable seeds inside after several years, but like many gardeners, I gather my own seeds at the end of the season and dry them for the future. Eureka! Yes, it can be done by anyone, and it IS done, all the time. There's no magic to it, save for making sure the seeds are thoroughly dry before storing. What's more, the amount of seeds to be found in just a few ripe flower heads (mature and dry) is mind-boggling and can fill many paper envelopes to bursting. What a tremendous value!
Probably one of the most delightful discoveries of gardening is to find that many flowering annuals self-sow. The flowers mature and drop fertile seeds throughout summer and fall. Some of these seeds will sprout at the end of the gardening season, and the rest remain dormant under the snows of winter. When spring arrives, and the budding gardener anxiously gets out to hoe the flower bed for spring planting, Eureka! Lots of tiny seedlings await his or her gaze. The job is already done.
This is one reason for waiting to work up your existing annual flower beds each spring. It's not laziness; it's expectation. If you've seen it once, it's an amazing thing: Through no effort on your part, last year's annual flower bed springs forth once again via seeds that you did not plant. All that remains is to manage the bed by thinning and a bit of transplanting.
I do not cover the empty spaces in my annual flower beds with mulch for this very reason—to create a seed bed. Though it's more work to weed the bed all summer, I like to accommodate next year's offspring.
Just as a disclaimer, not all annual flowers can be counted on to duplicate their parents in appearance, but many can and do—willingly!
Perennials are the flowers that truly "come back" each year. They live year-round and then burst into bloom in the spring or summer for a few weeks of their own special glory time before becoming foliage plants once again. Discovering that such everlasting flowers exist is a rewarding moment.
Flowers that come back each year eliminate a lot of yard work. Eureka! Put them in once and then virtually forget about them. They grow steadily over the years to ensure that there will always be something blooming in the yard. This is a welcome relief to the gardener who only knew about annual flowers before.
With practice, a new gardener can learn the bloom times for various perennials so that when one type is in bloom, the other type is budding and will follow suit in a week or so. This makes for continuous blooms that can be enhanced with the addition of annual flowers placed here and there. A word of advice: Perennials have a tendency to overrun any spot where they are planted. Many times, an annual flower bed becomes a perennial bed with the innocent addition of just one perennial specimen. Better to put annuals in a perennial bed than to put perennials in an annual bed. Eureka!
When I was young, I thought that a trip to the store was necessary to get a new houseplant each time I wanted another one. Then, an experienced gardener taught me about cuttings. She took me to her picture window so I could watch as she snipped a few stems from a purple velvet plant. I was a happy camper filled with wonder on the drive home with a plastic pot of soil and fresh, fuzzy stem cuttings. After a few days, I knew the purple velvet cuttings ‘took' when they transformed from limp to rigid. Eureka! Free plants!
Intrigued, I tried it myself: mimicking my gardener friend, I cut a few stems from my arrowhead plant and stuck the stems in a jar of water for rooting as instructed. Okay, so the stems were REAL long, and the new plant looked awkward after it was potted in soil, but it was a success because I was learning.
Two things awakened in me back then: appreciation for the miracle of the replication of life, and a sense of honor to participate in that process. So this is the inspiration that drives gardeners to do what they do. Eureka!
- Shake down your plants for free seed: an introduction to collecting seeds by Jill M. Nicolaus (critterologist) 10/16/2008
- Spring is Here, Don't Touch That Spade!!! by Lee Anne Stark (threegardeners) 3/25/2011
- Perennials demystifed by Sally G. Miller (sallyg) 4/28/2011
Related Dave's Garden Discussion Forums for more information and ideas:
Endnote:  Merriam-Webster Collegiate Dictionary (11th edition; Merriam-Webster, Incorporated, © 2004) p. 431