My understanding of portable softare is that it's simply anything coded so that it can run from removable media such as a USB thumb drive, for example. In the context of my experience, it also leaves no trace of usage behind on the host machine that portable media is connected to - portable browser, email client etc. And, yes, it is legal.
As for cracked software, are you serious? That is software which has had the copy protection broken so as to run without a commercial license being required. And, yes, it is illegal.
Ditto what happygeek said .and its nothing new ,i first connected to the internet in 1996,and there was all kinds of cracked programs avaible ,maybe not portable apps, will also like to add seeing as you are new to computers[lol] and whats outthere might i suggest Googlehappy hunting .
i use to have a thumdrive full of portable apps ,like firefox and much much more ,a email program .i could plug in the thumb drive into anyones computer check my mail ,surf the net and not add a single thing to anyone computer while doing this ,great stuff actually
Cracked software distribution pre-dates the Internet, of course. The cracking groups, also known as Demo groups at the time IIRC, on the Amiga (and to a lesser extent PC and Atari) platform existed to break copy protection on software and then redistribute either by post or BBS.