The sense of "might" there is similar to saying "it is now 6pm. The store across the street closes at 8pm. I think I'll go there now, that I might get some shopping done while there is still time, and so I won't have to rush, and forget some things."
In other words, as used there in that verese, the word "might" refers to what was now theirs due to His action, right before that - He expounded or broke things down unto them.
How?
In the same way Mid-Acts Dispensational Bible Study does - via taking them to the various passages and basically saying "see this here; this is speaking of Me; and see this verse over here: same thing. And this verse over here; and this one; and so on.
You see that here, as well...
Acts 17:2 And Paul, as his manner was, went in unto them, and three sabbath days reasoned with them out of the scriptures, 17:3 Opening and alleging, that Christ must needs have suffered, and risen again from the dead; and that this Jesus, whom I preach unto you, is Christ.
17:11 These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so. 17:12 Therefore many of them believed; also of honourable women which were Greeks, and of men, not a few.
As with that; the Lord was simply pointing out one verse and then to another verse that would shed some light on that other one, towards opening up, or laying out before the eyes of their understanding, the intended sense of a word, a phrase, or a passage.
Luke 24:27 And beginning at Moses and all the prophets, he expounded unto them in all the scriptures the things concerning himself.
24:44 And he said unto them, These are the words which I spake unto you, while I was yet with you, that all things must be fulfilled, which were written in the law of Moses, and in the prophets, and in the psalms, concerning me.
The word "should" is also used like that, at times.
Anyway, hope that helps, some, bro.