Hi dimitris,
TWebBrowser in Delphi is ActiveX control which dock Internet Explorer so it works only on windows (I think this controls exists for Lazarus too)
THtmlPort - this is native pascal implementation rendered by LCL, so it is multiplatform (windows, linux GTK, QT). Similar to this component is TIpHTMLPanel from TurboPower, you find example of it in lazarus_dir/examples/turbopower_ipro (you probably need instal TurboPowerIP package from menu Package -> Configure Installed Packages, I don't remember if this package is installed by default). Notice that this controls have only basic HTML (4.0?) support, no java script etc, you must do it by your self, even sockets to preview pages online
Gecko - This is full FireFox engine with everything what you need, it works similar like TWebBrowser on delphi. But this browser (gecko engine) is not installed on system by default (like TWebBrowser = Internet Explorer) so you need install xulrunner (mozilla sdk) or include it in your application installator
Details you find in links which Phil posted
Regards