Examples using Select and Cases:

In[1]:= m = Table[RandomInteger[], 10, 4]
Out[1]= {{0, 0, 1, 0}, {1, 0, 0, 1}, {0, 1, 1, 1}, {0, 0, 0, 1}, {0, 
  1, 0, 1}, {0, 0, 1, 0}, {0, 0, 1, 1}, {1, 0, 1, 1}, {1, 1, 1, 0}, {1, 0, 0, 0}}

In[2]:= Select[m, Last[#] == 1 &]
Out[2]= {{1, 0, 0, 1}, {0, 1, 1, 1}, {0, 0, 0, 1}, {0, 1, 0, 1}, {0, 0, 1, 1}, {1, 0, 1, 1}}

In[3]:= Cases[m, {_, _, _, 1}]
Out[3]= {{1, 0, 0, 1}, {0, 1, 1, 1}, {0, 0, 0, 1}, {0, 1, 0, 1}, {0, 0, 1, 1}, {1, 0, 1, 1}}

This form will also work:

Cases[m, {__, 1}]

The & denotes that what's before is the body of a pure function. One can also say that it is a shorthand for Function. These forms are equivalent:

Select[m, Last[#] == 1 &]

Select[m, Function[Last[#] == 1]]

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