Nellie B. Nicholson was born in Baltimore, Maryland, on July 22, 1888, the youngest of five children of George W. and Charlotte Nicholson. George was born into slavery in 1845. After serving in the 39th Regiment Maryland Infantry as part of the United States Colored Troops during the Civil War, he was freed in 1865. He went on to work as a waiter and a janitor, according to census records. Charlotte was born around 1849 and worked as a skilled seamstress and dressmaker. After attending Baltimore Colored High and Training School, Nellie moved to Providence, Rhode Island, in 1906 to attend the Women's College in Brown University. She received her AB degree in 1911.

While in Providence, Nicholson lived at the Working Girls Home at 105 Bates Street in the Lippitt Hill neighborhood. She then became a boarder at the Home for Aged Colored Women at 45 East Transit Street. Both locations required Nicholson to commute over two miles round-trip due to Brown's housing segregation policies that barred Black students from living on campus.

Upon completion of her studies, Nicholson returned to Baltimore to join the faculty at the Colored Training School, teaching Education, Arithmetic, and English. By 1914, she had moved to Wilmington, Delaware, to fill a position as Mathematics teacher at Howard High School, where she also later, and briefly, taught English. In Wilmington, she lived on East 10th Street, where so many Howard School teachers lived that students referred to it as "Teachers' Row." The 1920 census found her living in the household of Caroline B. Williams, Howard's geography teacher, at 202 East 10th Street, where other residents included another teacher, Helen Henderson, a Howard High School student from Maryland, Cora Berry, and Caroline Williams's sister, Elizabeth Williams Tyler, a nurse staffing a local health clinic. After her 1928 marriage to William H. Taylor, a widower with three children, Nicholson continued to teach at Howard High School, commuting daily from her new home in Philadelphia until her husband's sudden death in 1930, when she returned to live in Wilmington. Two of her stepdaughters then attended and graduated from Howard High School. Nicholson undertook further study at the University of Pennsylvania, receiving her master's degree in mathematics education in 1931 with a thesis on the teaching of algebra. She completed additional coursework toward a doctoral degree but did not finish a dissertation. After a brief stint as advisor for girls at the high school, she was promoted to vice-principal in 1931, an appointment she filled until her retirement in 1958.

During her teaching career, Nicholson was surrounded by many other fellow teachers and college-educated women. This led to her involvement in groups such as the Zeta Omega chapter of Alpha Kappa Alpha Sorority, Inc., in Wilmington, of which she became the second chapter president in 1923, following her colleague, Oberlin College graduate, Anna Brodnax. For the National Association of College Women, of which Brodnax was vice-president, Nicholson served on the executive board, beginning in 1925, and became a life member in 1943. With another colleague, Sadie L. Jones, she founded a local Delaware affiliate, the Women's College Club of Delaware. The group dedicated itself to improving the "educational condition of Negro girls," ending "dormitory discrimination," promoting "equality of opportunity," and sponsoring scholarships for African American college women. In 1925, she also joined the National Council of Teachers of Mathematics, one of only ten Delaware teachers who belonged to the association.

Howard High School teachers formed a core element of the Equal Suffrage Study Club, founded in March, 1914, at the home of Nicholson's neighbor, Emma Gibson Sykes. Nicholson was a founding member. With Howard's renowned English teacher, Alice Ruth Moore Dunbar (later Dunbar-Nelson) as president, the group quickly organized to study and agitate for Black women's voting rights, meeting regularly, marching as a separate unit in Wilmington's first suffrage parade in May 1914, and lobbying for both state and national suffrage amendments until 1920. Once the Nineteenth Amendment was ratified, the Suffrage Club reorganized in order to encourage African American women to register and vote. Many of the Suffrage Club members were also involved in initiating a Wilmington chapter of the NAACP, chartered in January 1915. Along with colleagues Alice Dunbar, Caroline B. Williams, and Alice G. Baldwin, Nicholson signed on as an early supporter and agreed to take charge of press relations for the fledgling group. She remained an active member for decades, during which the group successfully protested the screening of the film "The Birth of a Nation" in Wilmington, campaigned to get newspapers to capitalize the word "Negro," worked to ring in justice through lawsuits seeking fair treatment in jobs and equal benefits for Black soldiers, and supported the Dyer anti-lynching bill.

Throughout her years as Howard High School vice-principal, and after retirement, Nicholson was heavily involved in the Wilmington community. She was a long-time member of St. Matthew's Episcopal Church, where two colleagues in the Equal Suffrage Study Club, Blanche Williams Stubbs and Emma Gibson Sykes, also worshipped. She gave time to the Red Cross, the United Negro College Fund, and the Wilmington "colored" YWCA, of which she was a founder in 1935. She was also the President of the New Castle County Retired Teachers' Association. In 1957, as Delaware was responding to a Supreme Court order to desegregate its schools, and shortly before she retired, she took the lead in facilitating conversations across racial lines at a three-day conference of the Delaware Council of Churches and United Church Women of Delaware.

Nicholson died in her Wilmington home, 1509 West 6th Street, on December 20, 1965. She was buried in the historic Eden Cemetery in Collingdale, Pennsylvania, the final resting place of her late husband and notable human rights advocates including James Forten, Frances Ellen Watkins Harper, and William Still. Her estate, valued at almost $12,000, was managed by lawyer Louis Lorenzo Redding, who in the early 1950s had prepared and argued three major court cases leading to university and public-school desegregation in Delaware, and who, in his youth, had been her neighbor on "Teachers' Row" and her student at Howard High School. Nicholson emerges as a trailblazing force that transformed her community. At the same time, her life reflects the high standards of leadership and service typical of Brown University graduates past and present.