Irregardless is an informal (and erroneously created) word meaning "regardless." If you felt sick but were determined to make it to your bowling tournament anyway, you might say, "I'll be there with my bowling shoes on, irregardless of how much I'm sneezing and coughing."
Although irregardless often gets used to mean "regardless," it's considered highly informal, if not flat-out wrong. Irregardless probably grew out of a combination of the words regardless and irrespective, and it's been used ever since the 18th century as a humorous or over-emphasized version of regardless. If you want to be taken seriously, though, leave off the ir- at the beginning.