A seed is a plant embryo, plus nutrient tissues to feed the embryo, packaged in a protective shell. Since it's an embryo, it's the product of sexual reproduction.

Here's how it works.
When a seed germinates, a plant grows out of it. It's only partially true to say that flowers form from seeds because, actually, the whole plant forms from the seed. Even many non-flowering plants like pine trees come from seeds. After the plant matures, it reproduces. For flowering plants, that means they make flowers to attract pollinators. Pollen is delivered to flowers by bees, wind, or a number of other "vectors." Sperm cells leave the pollen and fertilize the eggs, which are found deep inside the flower. The outer parts of the flower (the parts we think are pretty) then die, but the inner parts that contain the fertilized eggs develop into fruit. All fruits contain seeds (so tomatoes and zucchinis are fruits, not vegetables). The fruit's job is usually either to provide food for the baby plant or to tempt an animal to eat the fruit, spreading the seeds in the process. Once the seeds are out of the fruit and into the ground, they grow into new plants.

I hope that answers your question!

I will here ignore the (potentially complicated) process by which a pollen grain gets to an ovule; it may be by wind or the pollen grain may travel via a pollinating organism. In any case, when the sperm reaches the ovule it fertilizes the egg to form a zygote which develops into a young embryo. As this proceeds, the embryo and its associated nutritive cells enlarge, and so does the protective integument.

As the embryo plus nutritive reserves reach maturity, the integument generally becomes hard and resistant and is then refereed to as a seed coat. The whole structure (embryo, food store & integument) is then referred to as a seed, which may be dispersed by wind or animals, thus spreading the genotype of the plant over the surface of the Earth. The same process, with certain variants, occurs in other groups of plants that bear seeds (e.g., pine trees, cycads, etc.)

Seed plants (not just flowering plants, but not all plants) have organs called ovules where they are going to produce seeds. The ovules are fertilized by pollen, and then mature and grow to become seeds. In a flowering plant, the ovules are contained within the ovary, which is a bulbous structure at the base of the flower. In a seed plant that is not a flowering plant (such as a conifer), the ovules are located inside of the scales of the cones.

Consider the example of an apple. The fruit is the ovary, which has grown and enlarged after fertilization of the ovules (which have become seeds). The flower, what is left of it (the petals have all fallen off), is still on the apple - on the end of the apple opposite the stem.