Hopefully this will help; I'll try to be as non-partisan as I can be, and answer a few other questions aswell.

What is it?

Quoting gov.uk:

"Non-domiciled" residents are UK residents whose permanent home (domicile) outside the UK may not have to pay UK tax on foreign income

If you don't earn more than £2,000 overseas and don't transfer this to a UK account, then you don't have to pay a charge to obtain this privilege.

Those who either transfer foreign income to a UK account or earn more than £2,000 outside the UK may choose to pay tax or pay a charge of £30,000 to avoid the tax, but lose tax-free allowances on Income Tax and Capital Gains taxes. Note that to do this you have to be resident of the UK for 7 out of the previous 9 tax years, with the charge rising to £50,000 if you have been resident for 12 out of 14 previous tax years

In effect; those who normally live outside the UK don't pay tax on income earnt outside of the UK, provided they follow certain conditions.

Will it increase/decrease revenue?

This is quite debatable. At the moment, we currently receive the annual £30,000 and £50,000 charges from non-domiciles. The suggestion is that by abolishing non-domicile status, you potentially get more money through tax than you would through charges, as often those with non-domicile status are the "super-rich"; Roman Abramovich is an example of a super-rich person having non-domicile status

The problem that's been suggested however is that we could potentially see these super-rich people leave the UK to go to other places as they don't want to pay more tax; the UK relative to other countries is often seen as a bit of a tax-haven because of non-domicile status, but that doesn't mean there aren't other places these people can go (Switzerland comes to mind). If the exodus was large enough, then it could potentially reduce revenues, although its impossible to predict exactly how many people will leave.