Undertaking in general means an agreement to be reponsible for something. In a legal context, it typically refers to a party agreeing to a surety arrangement, under which they will pay a debt or perform a duty if the other person who is bound to pay the debt or perform the duty fails to do so.
The following is are examples of state laws dealing with undertakings:
(a) Not later than 15 days after the third-party claim is filed with the levying officer pursuant to Section 720.120 or 720.220, or 15 days after filing an undertaking pursuant to Section 720.610, either the creditor or the third person may petition the court for a hearing to determine the validity of the third-party claim and the proper disposition of the property that is the subject of the claim. (b) The hearing may be held whether or not an undertaking has been filed but not if a deposit has been made pursuant to Section 720.260. (c) The hearing shall be held within 20 days after the filing of the petition unless continued by the court for good cause shown.
11.16.070 Filing an undertaking. In lieu of making either a general or special deposit, or to supplement a general deposit not sufficient in amount, the moving contractor may file an undertaking with the commissioner in a penal sum not less than one thousand dollars, executed either by two good and sufficient sureties or by a corporation incorporated for the purpose of making, guaranteeing, or becoming a surety upon bonds or undertakings, complying with Section 1056 of the Code of Civil Procedure, and by the moving contractor conditioned upon the payment of all fees and other charges required by this article, which may become due because of any permits issued during a period of not less than one year.
27-18-302. Filing of undertaking -- sheriff's liability. The sheriff shall thereupon file said undertaking with the clerk of the district court out of which said writ of attachment emanates, and such sheriff shall thereupon cease to be liable under said writ, and any and all actions on such undertaking shall be against the obligors named in such undertaking.