All meetings we do start with a check-in, and end with a check-out round. This is embedded in Holacracy, but also in older systems like Sociocracy and many older tribes and religions. At ⚽Tactical meetings and Governance meetings meetings, the slogan for it is: "Call out distractions, get present".
The simplest and hardest rule of the check-in and -out is that only one person speaks. Others don't respond or ask questions, however well-intentioned they are. The meeting facilitator guides it by giving people the word one by one, or you can just see who wants to speak, or let people point at the next person to check-in or out.
We used check-in at the beginning of a meeting mostly to make a conscious transition from where you came from (private or work), into the goal of and your role in the meeting. It also helps to create a shared feeling that everybody has a more or less equal rolein the meeting, and that they are all here to contribute even if they are not the "boss".
The value of checking-in in meetings
For us, the value of a check-in in the beginning of a meeting is to set the expectation that everybody is really present. Nobody is on their phone or laptop, or still busy with the past meeting, in their head. We're here to accomplish something in an efficient manner. If you can't be that present, you shouldn't be present. It also helps to set expectations, or to temper them when you hear others may be distracted. This prevents potential frustration and thus makes the meeting more efficient.
The value of checking-out of meetings
For us, the value of the check-out was in sharing reflection so that the meeting can be improved next time. Of course, there is no space to actually do something right away during the check-out, but any tensions raised will find their way into a future improvement. Also, it really helps to hear from others how they felt about the meeting, and with what kind of feeling they continue about their day. You leave the meeting feeling more connected and united.
Wrong assumptions
For both check-in and check-out, you'd be surprised how often your assumption about how someone is feeling or thinking, is actually wrong. These little adjustments of the way you see reality, help cut the waste in all other interactions at work.