Quote Originally Posted by Sir Bahamut
SeeD doesn't mean a thing in the world.

Just pause to consider how Edea thought of the name.
That's right, she got the name SeeD AND Garden from Squall, when he returned to the past.
Squall gave her the names, she then founded Garden and SeeD, leading Squall to give her the names.
Since Squall had no idea of any meaning, Edea obviously didn't either, hence they mean nothing.

It's a weird timetravel situation, but that's how it is.
But where did the original idea of SeeD come from? This is the most widely
used rhetorical question when it comes to time travel theory, though it's
usually:

A young inventor is trying futilely to build a time machine in his garage.
Suddenly, an elderly man appears from nowhere and gives the youth
he secret of building a time machine. The young man then becomes
enormously rich playing the stock market, race tracks, and sporting
events because he knows the future. Then, as an old man, he decides
to make his final trip back to the past and give the secret of time travel
to his youthful self. Where did the idea of the time machine come from?

And an even cooler one:

There is also the paradox of the man who is his own mother. (My
apologies to science fiction writer Robert Heinlein.) "Jane" is left at an
orphanage as a foundling. When "Jane" is a teenager, she falls in love
with a drifter, who abandons her but leaves her pregnant. Then disaster
strikes. She almost dies giving birth to a baby girl, who is then
mysteriously kidnapped. The doctors find that Jane is bleeding badly,
but, oddly enough, has both sex organs. So, to save her life, the
doctors convert "Jane" to "Jim."

"Jim" subsequently becomes a roaring drunk, until he meets a friendly
bartender (actually a time traveler in disguise) who wisks "Jim" way
back into the past. "Jim" meets a beautiful teenage girl, then
accidentally gets her pregnant with a baby girl. Out of guilt, he kidnaps
the baby girl and drops her off at the orphanage. Later, "Jim" joins the
time travelers corps, leads a distinguished life, and has one last dream:
to disguise himself as a bartender to meet a certain drunk named "Jim"
in the past. So, who is "Jane's" mother, father, brother, sister,
grandfather, grandmother, and grandchild?

.opt