How to check if an element in a cell array is unique or repeated

Use unique for this purpose, it can work on cell arrays too:

[U, ic, iu] = unique(C);

Where C is your cell array. U is a new cell array with the same values as C but without repetitions. You can then count the occurrences of each value using histc:

[U, ic, iu] = unique(C);
count = histc(iu, 1:numel(ic)) 

Example

For the sake of the example, let's generate a random cell array of strings first:

strings = {'foo'; 'bar'; 'baz'; 'bang'};
C = strings(ceil(numel(strings) * rand(6, 1)))

This should generate something like this:

C = 
    'bang'
    'baz'
    'foo'
    'bang'
    'bar'
    'foo'

Now we count the occurrences of each value in C:

C = strings(ceil(numel(strings) * rand(6, 1)));
[U, ic, iu] = unique(C);
count = histc(iu, 1:numel(ic))

This should result in:

U =
   'foo'
   'bar'
   'baz'
   'bang'

count =
    2
    1
    1
    2

which means that 'foo' and 'bang' are repeated twice, while the rest only once, which is correct.
If you are only interested in the truly unique values, you can do:

U(count == 1)

Which should return in our example:

'bar'
'baz'

Note that each element in count represents the corresponding value in U (not strings, they may have a different order).