irregardless / regardless
Standard English uses regardless; irregardless is nonstandard.
The two words mean the same thing. Irregardless adds the negative prefix ir- to a word whose suffix -less already makes it negative, so the prefix contributes nothing. Many people judge a speaker who uses irregardless as careless, and the word has no place in standard English.
Irregardless most likely blends regardless with irrespective, a standard word of the same meaning. Its listing in dictionaries records that people use it; the listing does not make the word standard.
Examples
Use Regardless of the weather, the parade will start at noon.
Avoid Irregardless of the weather, the parade will start at noon. (The prefix ir- in irregardless adds a redundant negative. Write Regardless of the weather, the parade will start at noon.)