With an umbrella company you become an employee of the umbrella company and are paid after deduction of PAYE (Income Tax) and National Insurance. There are some tax benefits in that you can be reimbursed tax free for some expenses such as travelling to and from your client, food and drink when at the end client/travelling and any accommodation costs.
A more tax efficient way is to run your own limited company as this allows you to pay yourself a small wage tax free and take the remainder as a dividend. In some instances it is also possible to utilise the tax allowances opf a partner or wife/husband. With this method it is important you are outside the scope of IR35 and are genuinely "self employed". It also depends how long you expect to be contracting for.
The reason clients and recruitment agencies require you to do one or the other and not just pay you direct is because they don;t want the responsibility of you being deemed as their employee and also if you were to avoid tax they could be held liable. SOme agencies will pay you after deducting full tax but this is usually the most inefficient way.