It's a nugget of inspiration, that comes to you at odd times. Every songwriter, lyric writer, has a collection of ideas somewhere, probably in their phone like me. Ideas of songs to be, themes, concepts. Sometimes it's a complete melody, a whole chorus that comes to you, complete. Sometimes its just one line and sometimes it's just a idea for a song, a feeling.
I don't think you can go looking for inspiration. You can put yourself in a better position, keeping your mind clear, relaxing, going to a happy place, or at least emotionally quiet. And let ideas come to you, don't search, don't seek. We can tell when someone is trying too hard, when you're out of ideas and this is the best you could scratch up. Let things come to you and judge them from there.
I am always thinking. Thinking about life, things I have to do, things I want to do. I think about things I did, I've done, and wish I hadn't. I think about how things could've been different. I think about why things happen. Society is fascinating, but sociology even more. I'm totally amazed at the huge disconnect between most lives of humans and human nature, or nature in general. The gap between where we came from, living off the earth, fearing gods, in tune with nature, to now, sitting in chairs in cubes staring at screens.
Anyway, profound ideas come to me, things I want to share. Things about myself, bits of wisdom, even facts or truths that need to be said. My next thought is, will people want to hear this? Do I think people should hear this? Of course, this is a matter of opinion and I'm not always right, but this is the process.
These thoughts go on the list of ideas and begin to bounce around in my head. When the time comes, I'll find one that inspires me anew and get to work expounding.
If writing is your passion, you're always doing it. I'm always thinking, about new stuff or ruminating on older ideas. I'm not looking for song ideas specifically, but open to them. The more you generate, the more you have to choose from and the better they are. Now, they don't always turn into good songs, but there's a long, long way between the two.