Taproots tend to be straight, conical and tapered (think carrot). Lateral roots sprout from the taproot. Many weeds, such as dandelions, have taproots, which is why it is so important to pull them as soon as they are seen. The longer they are in the ground, the longer the taproot can get.
Many plants begin with a taproot, right after germination, but most monocots replace the taproot with a fibrous network, or adventitious, root system.
Growing plants with taproots in containers is usually a bad idea. As soon as the taproot hits the bottom of the container, the plant will be stunted and may die.
Most trees do not have a taproot. Pine and other confers, walnut, and hickory are exceptions to this rule.
Tomato plants grown from seed will develop a taproot, while tomatoes grown from cuttings will not. Cool, huh?
I hope this information inspires you to grow more of your own food. You can ask your garden questions on my Home page.