The word trouble occurs sixteen times in the Book of Mormon, seven times as a noun and nine times as a verb.
As a noun, trouble is sometimes paired with "care and sorrow" (Alma 40:12), and more often in the plural with trials and afflictions (Mosiah 29:33; Alma 36:3, 27; 38:5). In the Isaiah passages, it is paired with "darkness, [and] dimness of anguish" (2 Nephi 18:22), where it translates the Hebrew ṣārāh, which is the feminine abstract of ṣār, meaning enemy, oppressor, persecutor, and would thus mean something like enmity, oppression, persecution.
The root of the Book of Mormon use of the word seems to be the verbal form, which is used in the sense of the earliest English use of the word meaning "To put into a state of (mental) agitation or disquiet; to disturb, distress, grieve, perplex" (according to the Oxford English Dictionary). The Book of Mormon expression reflecting this most clearly is "I have been somewhat troubled in mind" (Alma 22:3) or "Alma was troubled in his spirit" (Mosiah 26:10; cf. 26:13). It is used differently in such places as "being troubled no more for a time with their enemies." (Alma 3:24), but the main usage is being vexed in mind.
Various things could cause people to be troubled. One might, for example be "troubled because of the wickedness of the people of the house of Israel." (3 Nephi 17:14), or one could be troubled with "all the trials and troubles of a righteous king" (Mosiah 29:33). But one can also be troubled with intellectual issues, such as when Lamoni's father was "troubled in mind because of the generosity and the greatness of the words of thy brother, Ammon" (Alma 22:3). Alma's son was troubled by a number of intellectual issues which either were caused or exacerbated by his sins. His father sought to allay the intellectual issues, but counseled: "I desire that ye should let these things trouble you no more, and only let your sins trouble you, with that trouble which shall bring you down unto repentance." (Alma 42:29).
Productive trouble leads to revelation or repentance.