This movie has that muddy and dark animation that was so common in the 70's and 80's--and it's used here to great effect. Like with say, The Rescuers or The Black Cauldron, the literal dark coloration also goes along with the dark content. The movie isn't really about dinosaurs because it doesn't really teach anything about them, especially with the perspective of 32 years later (the T-Rex didn't stand like Godzilla, for one). Instead, it's about a young boy who loses his mother and has to go on a journey to find the rest of his family. Along the way, he meets unlikely friends who are very different from him. But their differences make them a stronger team as they strive together for what seems like an unattainable, though also absolutely necessary, goal.
The difference between the dinosaurs you can of course apply to any differences. To gender: it's Littlefoot and Cera who first meet. To race: Cera's father tells her that three-horns don't play with long-necks. To personality: Ducky and Petrie both having some timidity benefit from Littlefoot's leadership skills. Whatever differences you look at, the children use it to make them stronger as a group. They overcome obstacles by working together, each doing what they uniquely can do. Sometimes Cera's physical strength is just what they need or other times it's Ducky's swimming. A complete whole formed by unique, unified pieces.
What are they working towards? Their journey to the Great Valley to find their families and food is a practical one with a definite end. But it's basically an analogy for the journey of life. And that journey keeps on for a lifetime: we are constantly working towards that something. In a sense, we never really reach the Great Valley during our lives: our lives here are the journey. We're meeting people, forming relationships, overcoming obstacles, and keeping up hope. We remember the signs and keep moving forward to what is missing, to what we know is ahead.
Maybe that's why The Land Before Time became so popular. Not just because everybody loves dinosaur but because the story, in a wonderfully archetypal way, is in fact quite deep.