In my opinion, Luke presents the apostles as in the wrong when they took it upon themselves to choose a new apostlefootnote. Thus Acts 1b is important because 1) it establishes a contrast between the pre-Holy Spirit function of the church (it made poor decisions) and the post-Holy Spirit function of the church (Acts 15 - it made good decisions), 2) it emphasizes the God-ordained apostleship of Paul as opposed to the man-ordained apostleship of Matthias, 3) it follows up the story of Judas' death (by giving the church's reaction to it), which is an essential part of the narrative.
This is, of course, based on the assumption that Luke presents the church as being wrong to "ordain" a new apostle. If you disagree what this assumption, you will not agree with my interpretation of the importance of the passage.
Footnote: Reasons why I believe Luke presents the apostles as being wrong to choose Matthias as the new apostle (I will use only Luke's writings):
1) The apostles were told to "wait for the Promise of the Father" (Acts 1:4) in Jerusalem until they were endowed with "power from the Holy Spirit" (Acts 1:8). They were to "wait", which indicates that they were not to remain passive - especially when they were to wait until they received the power from on high. Jesus left them 40 days after his resurrection (which is ca. 42-43 days after passover, cf. Acts 1:3), and they received "power from the Holy Spirit" on Pentecost, about a week later. A week they were supposed to "wait" - and yet they took it upon themselves to spend that time choosing a new apostle.
2) Jesus was the one who chose the apostles - they did not choose themselves or each other (Lk 5:1-11, 6:12-16). Paul, however, was chosen by God.
3) According to Luke's own theology, there could only be twelve apostles (Lk 22:29-30, cf. also Mat 19:28). Paul is in Acts presented as an apostle (cf. i.e. 22:15, "For you will be His witness to all men of what you have seen and heard."; moreover Paul fits all the criteria for apostleship (having seen Jesus, receiving revelation from Jesus, performing miracles, preaching with authority, baptizing, etc.). A minor point I won't press is that Paul, who considers himself an apostle (cf. esp. Col 1:1 where he considers himself an apostle, and ch4 in which he sends greetings from Luke), spent a lot of time with Luke (cf. the "we"-passages in Acts). Thus, if Paul is clearly an apostle, Matthias cannot be - or else there would be 13 of them.
4) The arguments and methods by which Matthias was chosen is quite flimsy. The OT arguments are not direct OT prophecies about Judas, but rather generic passages about wicked men. Moreover, a lot is cast - the only NT reference to the "good guys" rolling a dice to decide stuff. And though they did pray about it, that does not automatically make their decision a good one.
5) Matthias appears nowhere else in the book of Acts - he is not mentioned again. This is an extremely weak argument, as most of the other apostles aren't mentioned again either. But it's worth noting.
Note: The fact that the text nowhere explicitly states that their decision was wrong is no counter-argument: Acts 21:12-13 say that the disciples urged Paul not to go to Jerusalem; Acts 15:36-41 say that Paul and Barnabbas had a disagreement without saying (directly) who was right.
Note: I consider arguments #1 and #3 to be the strongest - the rest are simply supporting observations which do not hold water on their own.
Note: One valid counter-argument is the use of the term "the twelve" in 6:2. However, this can be explained by the fact that Matthias was "numbered" or "counted" with the eleven (1:26) - this means that the apostles at that point in time considered him one of them, not that he actually was. Thus "the twelve" may refer to the "numbered" apostles, rather than being a technical term for the "true" apostles (cf. "the seven" in 21:8).
Bottom line: I'm pretty sure that Luke intended for us to consider the choosing of Matthias a mistake. But I'm not completely sure - let me know if I'm wrong!