It's generally assumed that during the evolution of lifeforms, there must have been some stage when single cells (unicelluar organisms) grouped together to form multicellular life.

There are at least nine different major theories regarding how (and why) this might have happened. See: Wikipedia

The subject is highly controversial - not least because, in terms of numbers of species, the vast majority of current lifeforms are uni-cellular.

Multicellularity allows an organism to exceed the size limits normally imposed by diffusion: single cells with increased size have a decreased surface-to-volume ratio and have difficulty absorbing sufficient nutrients and transporting them throughout the cell. Multicellular organisms thus have the competitive advantages of an increase in size without its limitations. They can have longer lifespans as they can continue living when individual cells die. Multicellularity also permits increasing complexity by allowing differentiation of cell types within one organism.
Whether these can be seen as advantages however is debatable.

[Source Wikipedia, as above]

However, the results of a set of experiments at Gatech (2013) suggest that the transition from a uni-cellular organism to a multi-celluar version may not be as great an evolutionary hurdle as was previously thought.

The research group were able to encourage about 10% of the population of a unicellular alga Chlamydomonas reinhardtii (which is believed to have never had a multi-cellular ancestor) to routinely clump together after 300 or so generations (in just 219 days).

In combination with recent work demonstrating the origin of multicellular clusters capable of Darwinian evolution, our findings suggest that multicellular complexity may evolve more readily than previously thought."

Source :Experimental evolution of an alternating uni- and multicellular life cycle in Chlamydomonas reinhardtii Nature Communications volume 4, Article number: 2742