ActiveX is an environment for running web applications and more dynamic content that regular HTML can't do. Often ActiveX is used to run forms, searching functionality, and email integration.
Unfortunately it's also a bit of a security risk since it can be used to execute viruses on a persons computer.
If you have IE (the only browser that supports ActiveX) you can turn ActiveX off. Without ActiveX, IE is much more secure. There's no reason to switch browsers over this.