Regularity is one of the factors by which individual Grand Lodges judge whether to recognise one another for the purposes of allowing formal interaction at the Grand Lodge level and visitation by members of other jurisdictions. Each individual Grand Lodge determines which other Grand Lodges it considers Regular (and the standards for determining this are not uniform between Grand Lodges). Since there is no globally centralised Masonic organisational system, and therefore the criteria for regularity are not consistent across all Grand Lodges.
The largest collection of mutually recognised Grand Lodges derives its regularity from one or more of the Home Grand Lodges – United Grand Lodge of England (UGLE), Grand Lodge of Scotland (GLoS) and Grand Lodge of Ireland (GLoI)) based on criteria known as “Basic Principles for Grand Lodge Recognition” which together they codified and published on 4 September 1929.
In the United States, each state has a Grand Lodge that supervises the lodges within that state and is sovereign and independent within that jurisdiction. These are commonly referred to as the “regular” or “mainstream” Grand Lodges. There is no national Grand Lodge. All regular Grand Lodges in the US are in mutual amity with each other and with UGLE.
In addition, most States also have a sovereign and independent Prince Hall Grand Lodge that is or was predominantly African-American. For many years the mainstream Grand Lodges did not recognize Prince Hall Freemasonry and considered them irregular. Starting in the 1980s, this situation has changed and today most mainstream Grand Lodges have come to recognize their Prince Hall counterparts and vice versa.
Due to a 19th-century argument and a resulting schism, not all Prince Hall Grand Lodges recognize each other (see Prince Hall National Grand Lodge), and generally the mainstream Grand Lodges have followed the lead of their Prince Hall counterparts when it comes to recognizing Prince Hall Grand Lodges in other states. UGLE has also granted recognition to Prince Hall Grand Lodges where they are recognised by their mainstream counterparts.
Throughout the US there are also numerous bodies that claim to be Masonic Lodges and Grand Lodges, but which are not recognized as such by UGLE, the mainstream Grand Lodges, nor their Prince Hall counterparts. These are deemed to be irregular.
More Info:
https://en.wikipedia.org/wiki/Regular_Masonic_jurisdiction