The word we are trying to define is "porneia".
A text which is helpful in defining this word is Acts 15:29, where the church in Jerusalem writes to the churches of the Gentiles to avoid four practices that are associated with idolatry: eating strangled animals, eating blood, eating animals sacrificed to idols, and "porneia" (sexual immorality). We know a lot about idolatrous practices of the time. For instance, we know that "temple prostitutes" in Corinth would lay with men, by which the man would gain the favor of the gods. Or the parties that would turn into orgies as they worshipped some pagan deity. Fertility goddesses were plentiful and often worshipped and elevated above other gods/goddesses. These sorts of sexual immorality would be everything from unmarried people having sex, to married people committing adultery. But always sex or sexual acts would be involved in these practices. Hence we can safely assume that this is what "sexual immorality" meant in Acts 15:29.
Another important text is 1 Cor 5:1, in which a man having sex with his step-mother is called "sexual immorality". One might wonder why the word "adultery" is not used here, for it certainly also applies. Indeed, often "fornication" and "adultery" occur together in the same lists of vices, indicating that the two words have two different emphases. I believe "porneia" is used in 1Cor 5:1 to emphasize the perverseness of the act. Thus "porneia" has the connotation of perverseness and extreme depravity.
A third text to consider is 1 Cor 6:18: Flee fornication. Every sin that a man doeth is without the body; but he that committeth fornication sinneth against his own body. This text tells us that "porneia" is basically any sexual sin, for all sexual sins are "against one's own body" (in the sense that one becomes one body with a person with whom one is not meant to be one.
In order not to be too wordy, I'll only briefly mention a couple of others: 1 Cor 7:2 tells us that "porneia" is not limited to adultery, but includes sexual relationships between unmarried people. Gal 5:19 and Eph 5:3 associate "porneia" with uncleanness, indicating the the sinfulness of it. These verses, and Col 3:5 and 2Cor 12:21, also associate "porneia" with lasciviousness/lewdness, which are not limited to physical sexual immorality.
In conclusion, "porneia" is any sinful act of sex. In the context of the New Testament, this is sex between any two people who are not married to each other. However, as hinted to in the previous paragraph, verses about sexual immorality should not be read as if they allow for sexual immorality that does not extend to the act of sex. Often Paul talks about thoughts, attitudes, intentions, and motivations are more important than external acts. Jesus mentions this same principle specifically in light of adultery, saying that a man may be guilty of adultery in his heart without ever showing any evidence of it.
In summary: "porneia", often translated "sexual immorality", means any sinful act of sex (i.e. sex between two people not married to each other). The word itself does not refer to non-physical immorality. However, when interpreting the intention and applying these verses, one cannot escape the conclusion that sexual immorality, though only concocted in the heart and never acted on, is sin.