Basically it is an adult who brings a lawsuit for the benefit of a minor.

What Nebraska calls a next friend is called a guardian ad litem in most States.

Here is the Nebraska statute:
Revised Statutes » Chapter 25 » 25-307
25-307. Suit by infant, guardian, or next friend; exception; substitution by court.
Except as provided by the Nebraska Probate Code, the action of an infant shall be commenced, maintained, and prosecuted by his or her guardian or next friend. Such actions may be dismissed with or without prejudice by the guardian or next friend only with approval of the court. When the action is commenced by his or her next friend, the court has power to dismiss it, if it is not for the benefit of the infant, or to substitute the guardian of the infant, or any person, as the next friend. Any action taken pursuant to this section shall be binding upon the infant.
From
http://nebraskalegislature.gov/laws/statutes.php?statute=25-307

http://legal-dictionary.thefreedictionary.com/Guardian+Ad+Litem
states:
"The concept of guardian ad litem grew out of developments in U.S. law in the late nineteenth century. Until then, the Common Law had severely restricted who could bring lawsuits in federal courts; it was easiest to sue in states through Equity courts. Changes in the 1870s relaxed these standards by bringing federal codes in line with state codes, and in 1938, the Federal Rules of Civil Procedure removed the old barriers by establishing one system for civil actions. Rule 17(c) addresses the rights of children and incompetent persons in three ways. First, it permits legal guardians to sue or defend on the behalf of minors or incompetent individuals. Second, it allows persons who do not have such a representative to name a "next friend," or guardian ad litem, to sue for them. And third, it states that federal courts "shall appoint a guardian ad litem for an infant or incompetent person not otherwise represented in an action or shall make such other order as it deems proper for [his or her] protection." In practice, the courts have interpreted this last provision broadly: the term infants is taken to mean unborn children and all minors. In addition, courts can exercise discretion; they are not required to appoint a guardian ad litem."

http://www.legalview.com/Legal-Dictionary/Next_friend/Default.aspx
states:

"Legal Dictionary - Next friend

Someone who appears in court in place of another who is not competent to do so, usually because they are a minor or are considered incompetent. Often the role is filled by a parent or other relative; it can be any legally-competent person whose interests do not run counter to those of the person on whose behalf they are acting . The "next friend" is not a party to the proceeding, nor are they a formally-appointed guardian. Instead, they are considered an agent of the court whose role is to protect the rights of the incompetent person."

I hope this information is helpful.