Regarding the filibuster;
The rules for the Texas Senate state you must stand unaided, so no leaning or sitting. You can't eat or drink. You can't leave the chamber. You can't speak about anything other than the topic of the bill in question. You can't have any assistance from any other senators. You have three strikes before the filibuster is ended.
Senator Davis was struck out. The first 'strike' was when she brought up Planned Parenthood, which was judged (by the Republican majority in the Senate) to be off topic. The second 'strike' was when another senator helped her with her back brace (a neat trick if you are planning on standing up for thirteen hours straight). The third was when she was tying the law into the sonogram law proposed before.
After the third strike there were just under two hours of using parliamentary rules, challenges and questions to run down the clock. Basically the other Democrats stepped in to keep the vote from taking place. Senator Leticia Van de Putte (who had been at her father's funeral earlier in the day, and used that as a reason to ask for a review of the previous points of order), got in the best line. After some of her questions had been ignored and the final vote ending the filibuster was held she was recognised by the Speaker.
This was her question. At which point that cheering continued for the last fifteen minutes before the deadline, which is what blocked the vote from happening before midnight. There were attempts to take the vote but they failed. In the end, just after the deadline, they called the vote as completed and pretended it had been managed before the deadline.
When they did this there were ~180,000 people watching the Youtube livestream I was on. The official record was published with correct timestamps that were then changed (despite people having screenshots). Yeah, it was a pretty dumb attempt at fraud.
Maddow's report on this captures some of the feeling from the live stream and commentaries.As for why it matters;
The law would not only ban abortion after 20 weeks, it would shut down 37 of the 42 clinics that currently serve Texas. That's leaving five clinics covering the entire state. It would close every single clinic in West Texas. This would not just block abortions after 20 weeks, it would block all access to abortion for many women in Texas. Having to travel across or out of state is hard for a lot of women. Having to do so before the 20 week deadline, alongside other restrictions in this and other bills, is harder still.
Then there are the non-abortion services that will be denied with these clinics shut down. Many are also the primary healthcare providers in their area. This will flat out deny many people local healthcare.
Tying this back into the Voting Rights Act decision, I posted in the other thread how the Supreme Court decision paves the way for Texas to pass voting laws previously blocked by the VRA. One of those (albeit with other legal issues) is a new election map passed in 2011. This map deliberately gerrymanders Senator Davis' district out of existence. Basically without the VRA she wouldn't have her seat because the Republicans would have managed to split her majority-minority district into irrelevance.