The answer given by orthocresol explains (and also partly corrects) the name that was suggested by Wikipedia and was mentioned in the question; however, it deliberately does not discuss the correct name according to current (2013) IUPAC recommendations.
The resulting name ‘6-{[2-amino-2-(4-hydroxyphenyl)-acetyl]amino}-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0]heptane-2-carboxylic acid’ (ignoring stereodescriptors for simplicity’s sake) is actually not wrong; however it is not the preferred IUPAC name.
The difference concerns the ‘[2-amino-2-(4-hydroxyphenyl)-acetyl]amino’ substituent group. For the preferred IUPAC name, the locants ‘2’ for the amino and the 4-hydroxyphenyl substituents would be omitted since all substitutable hydrogen atoms of an acetyl group ($\ce{-CO-CH3}$) have the same locant, resulting in the name ‘[amino(4-hydroxyphenyl)acetyl]amino’. However, the preferred suffix for a substituent of the type $\ce{-NH-CO-R}$ is ‘carboxamido’ (i.e. ‘acetamido’ for $\ce{-NH-CO-CH3}$) rather than ‘acylamino’ (i.e. ‘acetylamino’ for $\ce{-NH-CO-CH3}$). Thus, the preferred name for the complete substituent group is 2-amino-2-(4-hydroxyphenyl)acetamido. (Note that the ocants ‘2’ for the amino and the 4-hydroxyphenyl substituents can no longer be omitted since acetamido has substitutable hydrogen atoms with different locants.) Therefore, the preferred name for the complete compound is 6-[2-amino-2-(4-hydroxyphenyl)acetamido]-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0]heptane-2-carboxylic acid.
To understand this name, we first have to see that the carbocylic acid group ($\ce{-COOH}$) is the principal characteristic group in this case. Therefore, this group is chosen for citation at the end of a name by means of a suffix. Accordingly, the senior parent structure of this compound is bicyclo[3.2.0]heptane-2-carboxylic acid.
The name of the parent structure is modified according to the positions of the hetereoatoms to 4-thia-1-azabicyclo[3.2.0]heptane-2-carboxylic acid.
Since the principal characteristic group is expressed by means of a suffix at the end of a name, the other substituent groups have to be expressed as prefixes. Considering only the groups that are directly attached to the parent structure leads to the name 6-acetamido-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0]heptane-2-carboxylic acid.
As mentioned above, however, the acetamido group has two further substituents: (a simple substituent group ‘amino’ and a compound substituent group ‘4-hydroxyphenyl’), which changes the acetamido group to the complex substituent group ‘2-amino-2-(4-hydroxyphenyl)acetamido’.