Summary

Electronic voting (also known as e-voting) is a term encompassing several different types of voting, embracing both electronic means of casting a vote and electronic means of counting votes.
Source: Wikipedia entry

Background

The Help American Vote Act (HAVA) of 2002, spurred the purchase of Direct Electronic Recording devices (DREs) because DREs were one way to satisfy the HAVA mandate of allowing the disabled to vote unassisted. DREs however are not the only way to satisfy that requirement and were not mandated per say.

Specifically HAVA states:
Section 301(a)(3):
(3) Accessibility for individuals with disabilities.--The voting system shall--
(A) be accessible for individuals with disabilities, including nonvisual accessibility for the blind and visually impaired, in a manner that provides the same opportunity for access and participation (including privacy and independence) as for other voters;
(B)satisfy the requirement of subparagraph (A) through the use of at least one direct recording electronic voting system, OR other voting system equipped for individuals with disabilities at each polling place;

Additional Links

FEC HAVA page
TX Secretary of State HAVA section

Other sites for further information:
Voting Rights Sites:
++ VotersUnite!
++ VoteTrustUSA
++ Election Line
++ Brennan Center for Justice
++ VerifiedVoting
++ Common Cause Election Reform Agenda
++ National Ballot Integrity Project
++ Electronic Freedom Foundation E-voting
++ Texas Safe Voting
++ ACLU-TX Liberty Blog
++ ACURATE; A Center for Correct, Usable, Reliable, Auditable, and Transparent Elections
++ Carter-Baker Commission on Federal Election Reform
++ Texas Secretary of State Elections Section
++ Texas Election Code
++ Congressman Rush Holt - H.R.550

Terms:
VVPAT – Voter Verified Paper Audit Trail
VVPAB – Voter Verified Paper Ballot