Marginal tax rates are the taxes that you pay on additional income. Eg., if I make (rounding numbers recklessly) £9k per year, I am taxed nothing. However every pound I make over £9k is taxed at 15% -- that's my marginal tax rate at the £10k income level -- then there is another step at £20k-something, etc.
For the poor, however, effective marginal tax rate include not only escalations in progressive tax rates, but the withdrawal of social support. Eg., let's say I am unemployed and receiving £700/month worth of benefits. Then I get a job which pays me £800/month. The first £750 is tax free, and I'll have to pay £8 of income tax on the remaining £50, so my total take-home pay is £792. Fair enough, so far...
Except now that I'm earning an income, all my benefits are withdrawn. This means that although I'm now doing £800 per month worth of work that I wasn't doing previously, at the end of the day I'm only receiving (£792 - £700 = ) £92 pounds of additional income. Hence my effective marginal tax rate on the extra income is a whopping 88.5%.
I'd have to think very hard about whether I wanted to keep that job, or stay on benefits. In fact, this is a fairly generous example: many benefits programmes are structured in such a way that they impose an effective marginal tax rate of more than 100% upon people who increase their incomes -- in other words, you can end up with less money by getting a job than by staying on benefits.
This is the mechanism which turns benefits programmes into poverty traps -- by de-incentivising people to work via astronomical marginal tax rates. Unfortunately, people have a very difficult time understanding this mechanism, and their intuitive reaction is often to "fix" benefits programs by increasing conditionalities and means-testing. The problem is that the more conditionalities and means-testing you impose, the more you increase the marginal tax rates for people trying to get out of poverty -- so such programmes are inevitably counter-productive.
A Unconditional Basic Income, however, is never withdrawn. This means that it imposes no penalties for increasing your earnings -- meaning that it actually minimises the effective marginal tax rates.
In fact a very fair basic income could be funded via a flat tax: tax every income at 50%, and then redistribute the earnings as a flat Universal Basic Income. Mean income earners, in this scenario, would pay exactly as much taxes as they receive back from the UBI -- so their tax rate would be zero. Non-income earners would earn 50% of the mean (which is roughly the level that Switzerland is proposing). Billionaires would see their income reduced by nearly 50%. However the marginal tax rate would be identical at every level of income. No matter what your standing in the economy, you would always receive the same UBI, and you would always pay the same rate of tax. It would seem almost fair.