"Satan" (Σατανᾶς) is from the Greek word satanas, which is an Aramaic and Hebrew word meaning "adversary," "opponent," or "one who opposes another in purpose or act." It is neither a positive or negative word, depending on who or what is opposed. Jesus uses it only thirteen times, but he uses it consistent with its Greek meaning but always in a negative sense.
Our word "Satan" is from the Greek form satanas from a Hebrew satan ( שטן) meaning "adversary," "opponent," or "one who opposes another in purpose or act. " The Greek version of this word appears initially only in thirteen times in Jesus's words. Interestingly, the Greek Septuagint usually translates the Hebrew word satan into the Greek word diabolos, which means "slanderer," (see this article) but which is translated in the English NT as "devils" or "demons." "Satan" is also translated to related words such as ἐπίβουλος, epívoulos, which means "treacherous." The Greek word Σατανᾶς appears for the first time and only time in the Greek OT at 1Ki 11:14. The story that features "Satan" most prominently, that of Job, the Greek word diabolos is used.
In my earlier work, I translated satanas, the Greek word translated as "Satan," as "adversity" or "adversary," which is the direct Aramaic meaning of the word, but more recently as "suffering" because many of the verses translate better that way.
Conflated with Other Words
Some insight into this word comes from where it is used in Mark 4:15 to describe who takes away the seeds sown by the wayside. In Matthew 13:19, this role is played by "the wicked one" from the adjective poneros, (see this article), which has more the sense of "the worthless one." Luke 8:12 uses the term diabolos, which is usually translated as "devil" but means "slanderous," (see this article). The term is also conflated with "Beelzebub," which is used to describe the master of devils (Matthew 12:27), but there it no association with the word satanas in the verse.
In the Greek Septuagint, the word diabolos is first used in Num 22:32, but the Hebrew word שטן is first used in Num 22:22. In this first occurrence, this word is translated into Greek as ἐνδιαβάλλω, endiabollos, which seems a variation on diabolos. In 1Sa 29:4, 2Sa 19:22, and 1Ki 5:4, this word is translated as ἐπίβουλος, epívoulos, which means "treacherous." The Greek word Σατανᾶς appears for the first time and only time in the Greek OT at 1Ki 11:14. After that, all translated of the Hebrew word seem to be to diabolos.
Part of the confusion about the "devil," "satan," and even "demons" is that the Gospel writers (Matthew and Luke) use this term to describe the person who tempts Jesus during his forty days in the desert. Though we do not have Christ's words describing this event, we know that it could have only come from his recounting it because he was the only one there. During the encounter, the term "devil" certainly applies, since the tempter seeks to get Christ to degrade himself, but at the end of the encounter, Christ addresses his tempter as "Satan," but he doesn't use this as a name (see below). It is simply as a description, "adversary." Since this story is clearly about a spiritual being (or one that inhabits the mind), the term "demon" also apply to the tempter, though Christ doesn't use that term any more than he uses the term "devil."
Satan" as Adversity
The meaning that Satan has today as the name of "the chief of evil spirits" comes from Christian traditions unknown at the time the Gospels were written. The Hebrew word was not a name, but a descriptive noun. King David is described as an adversary of his enemies with the term "satan." Even in the story of Job, where the adversary is personalized, the Hebrew "satan" is never used as a name, since it is used with a definite article ("the"), which Hebrew never does with proper names, "the adversary." More about the meaning of the Hebrew word from the Old Testament in this Bible Topics article.
In the Hebrew sense, "satan" means "an adversary" or more generally, "adversity" in the sense of "life's adversity" and, even more, "the accuser" in the sense of our inner voice of self-doubt.
Christ uses the word only three times in Matthew (Matthew 4:10 Begone, Satan! for it is written, 'You shall worship the Lord your God..., Matthew 12:26 And if Satan casts out Satan, Matthew 16:23 Get behind me, Satan). While he uses it to address someone twice, he does not use it as a name. This is an artifact of poor translation. In the Greek, the word is clearly not in the form of an address (called vocative) but in the form of an object of the verb. In other words, Christ is describing these people as an adversary, not calling them a name. The sense in the Greek in Matthew 4:10 is not "go away, Satan" but more like "take away adversity" or "take away a barrier."