An umbrella company is a company that is slotted in, as an extra contracting layer in between you, the worker, and the organisation you are working for. Using an umbrella company means that this organisation does not owe you any direct contractual obligations, for example to pay your wages, provide holidays and so on.
The umbrella company contracts with the organisation that provides the work, and then 'employs' you, the worker, to do it. As your 'employer', the umbrella company deducts PAYE tax and both employee and employer national insurance contributions from your pay packet. The umbrella company typically charges a fee, which can be as much as £30 a week.
Although workers have 'rights' under this arrangement, for example the right not to be discriminated against, or to receive the National Minimum Wage, these rights are owed to you by the umbrella company, not by the organisation for which you are doing the work.