It's nothing less than crucial. If it doesn't grab and hold the attention of an editor or that agent you've sent it to to try to get him or her to rep you, then you're already in trouble. If you have the chance to discuss things with an editor, most of them will tell you they must get hooked by the first sentence and caught up in the stroy within the first two or three paragraphs. If they aren't they won't read on. They can't. They have that whole humongous slush pile over there waiting for their attention. They can't keep slogging through your work in the hopes that it will be a sparkling jewel somewhere beyond a less than stellar beginning.
One way to get a feel for this is to read a lot of 'beginnings'. Check out other people's books. Grab one from your shelf now ( I know you have a lot of books right? - you're a writer).
Doesn't matter what genre you choose, what book you pick up. Open it at the first page and read the first sentence. Do you want to read more? I'll bet you do. I'll bet it's one of the reasons you got the book in the first place - it hooked you.
The title and the first line are of paramount importance to your story - even though it's likely the title will be changed somewhere along the line before publication.
Here are a few first lines chosen at random from a variety of books on my shelves:
What was he doing here?
It was a black night with barely a sliver of a moon to light the way. Samantha Cameron had been in the saddle for hours wandering in circles.
When I finally reached Tucson I felt like I was hauling half the dust of the desert along with me.
"I've watched through his eyes, I've listened through his ears, and I tell you he's the one. Or at least as close we we're going to get."
The cold should have made her shiver, but it was fear, terrible bone-chilling fear that seized Lara, causing such tremors they were impossible to control.
"Do you feel it boy? Do you feel the mist preparing?"
Death. Pestilence. Famine. They surround me, my lovers...
Okay, you get the drift. All very first sentences above. Now look at some more from your shelves. Those lines draw you in - first thing, right? The beginning needs to be short and sharp with no rambling. Condensed is good, rambling isn't.
Now is when you should jot down the very first line of your story. Think of this as an exercise. You may have to dash off anything that first comes to mind and then revise and refine it. Or you may give it a lot of thought and then write down the perfect first line. However you approach it, write it down and then ask yourself some questions about it:
1) Is it too long; so long the reader loses interest?
2) Is it to the point?
3) Does it hook the reader and cause that reader to want to read more?
4) Is there a bit of mystery to it? Does it give enough information to leave the reader wanting more?
5) Does it give too much information, again, risking losing the reader‟s interest?
6) Does it tease?
Okay, you get the idea. You're a writer. Get busy and write.