What is love, you ask? Prepare yourself for a wall of text. You have been warned.
Let's start at the right place and distinguish between different types of love. Naturally, love for a family member or a friend is going to be different from the love one feels for a romantic partner. I believe the OP is asking about the latter, so let's just focus on that.
The triangular theory of love is probably the easiest way to analyze this. It focuses on intimacy (closeness, sharing, and valuing one's partner), commitment (the decision to remain in the relationship), and passion (feelings of romance, physical attraction, and sexual desire). The ideal kind of love would be a combination of all three; this is what is known as consummate love. However, oftentimes we're lacking in one or two areas of the triangle, and we get different kinds of love that aren't nearly as fulfilling. Intimacy and passion without commitment gets you romantic love, which is probably more commonly known as lust. Intimacy and commitment without passion gives you companionate love, or friendship. Passion and commitment without intimacy and you have fatuous love, which is probably close to the obsession one feels when one has a crush on someone they've never even met. Commitment alone is an empty kind of love, intimacy on its own equates to simply liking the individual, and passion alone is a mere infatuation. The idea here is that all three are neccessary in equal measure to have true love.
Now, as for the body's physical symptoms of love; i.e. the sweaty palms, increased heart rate, flushed skin, dilated pupils, etc.? These can be explained by the cognitive-arousal model of love, as can the feeling of a 'rush' or a 'high'. In essence, the passionate component of love has interacting cognitive and physiological components. One experiences arousal as the 'rush', caused by the presence of someone one finds attractive, and one concludes that they must be falling in love.
For those who define love as a set of feelings-these feelings are caused by a sudden, heavy secretion of various feel-good hormones, such as oxytocin, serotonin, and dopamine. This isn't to say that these feelings are diminished in any way by recognizing what causes them; they are powerful no matter how one views them. People who describe love as 'mere' brain chemistry would be wise to keep this mind. I would include graphics to help explain everything here, but since this is my first post, you'll have to Google image 'triangular theory of love' and 'love chemistry' if you want them. They should help if things aren't quite clear.
As for me, personally...well, I can tell that I am at least in the process of falling in love right now. I don't think I'm quite there yet, but I intend to pursue my feelings and see this process through to the end, no matter how bitter that end may be. Despite how rationally I described love in the previous paragraphs, I'm actually a hopeless romantic. I'm totally addicted to romantic comedies, I dream of whispering sweet nothings in my lover's ear, and sharing everything I have and everything I am with that one special person.
"You are a beautiful, flawless flower, and I will be the sun that warms you, the rain that nurtures you, and the soil that holds you tight."
