Unilever Series

So what exactly is the 'Unilever' series? Like with many other galleries, it is just a series of exhibits by artists chosen by the Tate. In this case however, and unlike many other galleries who chose existing works by artists, the Unilever Series offers to the artist the vast space of the Turbine Hall in which to create a work of art, or in other words, the artist is commissioned to create something for that specific space.
'Unilever' is a company which produces various commercial hygiene products, such as Vaseline, Timotei Shampoo, Sure (deodorant products) etc. Due to their longstanding patronage and relationship to the Tate, they basically fund and enable the exhibitions in the Turbine Hall.
Here is what they say about their relationship with the arts:

Our commitment to the arts

Alongside our high-profile commitments to national organisations such as Tate Modern, The Royal Academy of Arts and The National Theatre, most of our arts expenditure goes to support the development of young talent, in line with our overall community programme.

Our 20-year programme of collecting contemporary art for our headquarters at Unilever House in Central London supports young and up-and-coming artists. A collection of modern art has also been established at our Home and Personal Care head office in Kingston. This is linked to a programme of employee development through creative workshops and community involvement, where members of staff volunteer to 'mentor' local arts organisations.

Unilever's commitment of £2.25m over eight years with Tate Modern has been extended to 2012. Our relationship with Tate Modern has enabled them to commission a new installation for the Turbine Hall each year. The eighth and most recent commission is by Doris Salcedo and opened on 9 October 2007.

As one of the Tate's neighbours on the Thames, Unilever was keen to support this enhancement to London's urban environment. The gallery has made a vital contribution to economic and social renewal in Southwark, bringing annual economic benefits worth £50-£90m, and creating up to 2,400 jobs. Each sponsored commission has a community and educational programme associated with it.