One reason that cells need to be close to one another is for cell communication. One way that cells communicate is via biomolecular transmitters. In order to signal a response, these cell are emitted from one cell and must interact with receptor proteins from the receiving cell. (The shape of the protein receptor and the emitted chemical signal fit together like puzzle pieces. This enables these protein receptors are specific in regards to the signals that are received.) Thus, the cells need to be close to one another so the biomolecuolar signals that allow for cellular communication can be easily transferred from one cell to another.
Interstitial fluid surrounds and bathes the cells. Interstitial fluid is the water solvent that contains water, salts, sugars, proteins, and other nutrients. Interstitial fluid helps to delivering such materials, cellular communication (via the means discussed in the previous paragraph), and the removal of wastes.
The proximity of cells within multicellular organisms help give the organism its shape. If cells were far apart from one another, the organism would not have a solid structure (much like the gas molecules that are used to inflate a balloon).