ILR is effectively permanent residency of the United Kingdom. It means you can settle permanently in the United Kingdom without any immigration controls. It is the last step before Citizenship.
"Indefinite leave to remain (ILR) is an immigration status granted to a person who does not hold right of abode in the United Kingdom, but who has been admitted to the UK without any time limit on his or her stay and who is free to take up employment or study, without restriction."
Most contractors will get it after 5 years on a Tier 2 Work Permit or a Tier 1 Highly Skilled Work Permit. You can work freely, study, and live throughout the United Kingdom. Any children that you have after having ILR status are automatically British Citizens.
After 1 year on ILR you can apply for British citizenship. If you are on Indefinite Leave to Remain and you spend more than 2 years outside the UK you may risk losing the status, however typically you can reapply for ILR to enter the UK.
When indefinite leave is granted to persons outside the United Kingdom it is known as indefinite leave to enter (ILE).