The Torah commands us to be kedoshim (holy, or set apart), requiring purity in what we eat, how we speak, what we wear, and how we behave. Tum'a is spiritual impurity generally resulting from transitions from life to death (even in a small measure; for instance—sleep or cutting nails). Tum'a inhibits or blocks us from achieving holiness.
Since we do not have a “red heifer” with which to make purifying water solutions, all people are considered to have some level of tum'a today.
Although there are three reasons to ritually wash hands--to add kedusha; to remove tum'a; and to remove dirt--tum'a normally has nothing to do with physical dirt. There are many types and levels of tum'a, with no exact progression. The following guideline is approximately in descending order from most impure to least:

Sources of the Different Levels of Tum'a

• Dead body (touching or being in same building with a dead body);
• Cemetery;
• Carcass of any dead animal not slaughtered by shechita;
• Women during and after menstruation or after childbirth (but before they immerse in a mikva);
• Sleep;
• Possibly a bathroom;
• Your hands' transferring tum'a to wet food;
• Your hands' transferring tum'a to bread;
• Food from under a bed on which someone slept;
• Intercourse or seminal emission;
• Having your beard, hair, or nails cut;
• Leather shoes;
• Touching body parts.

Depending on the level of tum'a, purifying may require:

• Washing your hands by the Three-Times Method.
• Washing your hands by the One-Time Method.
• Immersion in a mikva. OR
• Sprinkling with water that had been treated with ashes from a red heifer (which we do not have now).