Starting from the mundane, "your body is your temple" and so keeping it clean from the inside out to prepare it as a vehicle that will take you through your spiritual journey is an essential part of the yoga practice. Bathing, tongue scrubbing and a practice that I still need to learn how to do: the use of Jala Neti (Neti Pot)* are all essential to keeping the body clean. Cleanliness of the body from the inside includes making sure your food intake is pure as well as to include purifying practices such as pranayama (breathing) and asana (yoga poses) in your daily life.
The other obvious area of cleanliness is your surroundings, environment, place of worship etc.
Digging deeper cleanliness means purity. Purity of your actions of any violence, purity of your thoughts of any negativity and purity of your intentions of any ill will. Watch your mind like a hawk and you'll find that we are sometimes judgmental, sometimes negative, sometimes lazy, sometimes restless, sometimes dull, sometimes anxious, sometimes manipulative. Clearing your mind of unnecessary thought process and the repetitive non self serving inner dialogue is also a part of the cleansing process.
The thought process also affects how you vibrate in this world as an energy. You know that your vibrations are pure when you are joyful yet relaxed, vibrant yet peaceful. So your emotions and thoughts are a good mirror of the purity of your vibration. If you're still unsure of how to identify your vibration look at the experience you are having at a certain moment. If you can be content with it (even when it's "bad") then you're vibrating at a higher level. If you seem to be restless even in a calm situation, then watch your mind and see if you can accept how you're feeling at that time (which usually helps bring peace into situations) and watch how your experience transforms.
What you're trying to achieve through purification is a concept in yoga known as "Subanga Karamo": The body and mind at the most auspicious level to experience the self at high resolution. What does that mean? You're a diamond, you always have been and always will be. All you need to do is work through the dirt to find yourself. How? Iyengar advises:
"The impurities of the thoughts are washed off in the waters of adoration. The impurities of the intellect or reason are burned off in the fire of the study of self(…) with concentration, one obtains mastery over the senses. Then one is ready to enter the temple of his own body and see his real self in the mirror of his mind"
Shine on! :)
* Neti pots look like teapots to some extent, they are filled with salty water and this water is poured into one nostril and the water comes out of the second nostril clearing out passages and making breathing easier. Balanced breath is essential in the kundalini (enlightenment) process.