One's prakruti is one's constitution, the unique doshic balance that remains constant throughout a lifetime. It is like a fingerprint; everyone's is different. Vikruti refers to a current state of imbalance in one's prakruti. An imbalance can be caused by the seasons, by time of day, by improper food and lifestyle choices, etc. For instance, my prakruti is Vata-Pitta. My Vata is aggravated-that is my Vikruti. There are three doshas, and each person has a unique prakruti of either one dosha, or a combination of two, or all three.
The three doshas are vata, pitta, and kapha. Vata represents movement, pitta metabolism, and kapha growth and strength. Each dosha can be thought of as energies that are expressed through certain physical, mental, and emotional characteristics. There are certain diets, exercise plans, lifestyles, climates, and even colors that favor each dosha, and when one has a dosha in imbalance, either aggravated or deficient, there are such measures one can take to bring it into balance; that is, into what is considered balance for your own personal constitution.
There are questionnaires all over the Internet to help you determine your prakruti. It is best to fill out the questionnaires twice, once reflecting your usual state (you can think back to childhood to help you with that) and once reflecting your current state. This will allow you to see where you have an imbalance, if at all.