My first step when examining the search results from any online database is to learn more about the nature of the original source material. The US National Archives has selected articles from Prologue Magazine online -- one of which is The World War II Army Enlistment Records File and Access to Archival Databases Spring 2006, Vol. 38, No. 1, by Theodore J. Hull.
Note especially Hall's caution:
As with most archival records now used for genealogical research, the
records were originally created for a very different purpose than
identifying specific individuals.
Hall's article provides an overview of this source, including the purpose for which the information was collected, and discusses the migration path from the original index cards to its current home in electric format as part of NARA's Access to Archival Databases (AAD).
In the US Army, the term branch refers to what type of service the soldier is performing -- a list of modern-day branches can be found on the page Military Science at Hofstra University. Some examples are -- Infantry, Artillery, Aviation, the Signal Corps, Quartermasters, etc.
If you look for your relative in the database U.S., World War II Army Enlistment Records, 1938-1946 or at the US National Archives' own electronic database on their AAD (Access to Archival Databases) website, and the entry reads "Branch Immaterial - Warrant Officers, USA" it means that the Army wasn't assigning the recruit to a branch at that time. Dictionary.com and other online dictionaries define 'immaterial' as not pertinent; irrelevant.
The term 'Warrant Officer' refers to a military rank (and the corresponding pay grade).
Pay grades are used by the uniformed services of the United States to
determine wages and benefits based on the corresponding military rank
of a member of the services. While different titles or ranks may be
used among the seven uniformed services, pay grades are uniform and
equivalent between the services and can be used to quickly determine
seniority among a group of members from different services. They are
also essential when determining a member's entitlements such as basic
pay and allowances.
Pay grades are divided into three groups: enlisted (E), warrant
officer (W), and officer (O).
Wikipedia's article on Warrant Officers says:
On August 21, 1941, under Pub.L. 77–230, Congress authorized two
grades: warrant officer (junior grade) and chief warrant officer. In
1942, temporary appointments in about 40 occupational areas were made.
In his Prologue article, Hall says:
In general, the records contain the serial number, name, state and
county of residence, place of enlistment, date of enlistment, grade,
Army branch, term of enlistment, longevity, nativity (place of birth),
year of birth, race, education, civilian occupation, marital status,
height and weight (before 1943), military occupational specialty (1945
and later), and component of the Army. As noted earlier, at the end of
each "best guess" record appear the box and roll number of the
microfilmed punch cards.
But if your relative's entry in the database refers to a "Warrant Officer -- Branch Immaterial" it appears to mean that for the Army's analysis, the statisticians didn't need the information about what branch the service member was assigned to -- they were counting all the Warrant Officers as a single group.
More documentation on this database can be found via the National Archives' catalog -- see NAID 1263923, Electronic Army Serial Number Merged File, ca. 1938 - 1946.