It looks as though she registered the child and gave the father's name as Arthur Mayer (probably made up) and stated that she was married and called Jessie Mayer, nee Wicks (which she probably also made up). If the father's name was to be omitted, it only makes sense to omit the occupation too. The only Arthur Meyer I can find (in Lincolnshire) was born about 1894, and he measured fish for an occupation. Also they've omitted Wicks, which more or less proves that Jessie wasn't married when her son was born.
Who was James Mayer? In 1901 Jessie was a servant surname Mayer, in Lincolnshire, in 1891 she was an inmate in Boston workhouse with her mother Jane, sisters Ethel and May. The only James Mayer I can find doesn't seem to be connected, unless he is something to do with Jessie's father.
Have you got Jessie's birth certificate? The only one I can find is for a Jessie Mayers (with an S) in 1885 which fits with her age on various census. Her sisters Ethel and May are registered as Mayer, so Jessie's name could just be a misspelling. I doubt her mother was married either, as I can't find a marriage for a Mr Mayer to a Jane, although there is a marriage of an Arthur Mayer to an Ida Stephenson in 1882. There is no husband named on the 1891 census, although Jane Mayer states her husband is a railway worker. In 1901 she is very conveniently widowed.
Lizzie