TL;DR - the second of your explanations, mostly (it is a "point in time" evaluation, and not the final score the child will receive, most likely) - but it depends. This answer assumes United States based on the specific language used in the question, and will likely not apply to other countries' educational systems.
The Common Core, in the United States, has standardized the concept of skills-based grading, often using the term "proficiency" to indicate whether a student has met that standard. The other important change to many schools is a move towards grading that indicates whether a student is on track to meet standards, a "point in time" measurement, rather than a reflection of the student's work in and of itself over that time (as most of current adults are used to from our childhood).
Some skills are relatively short, and typically taught in a few days or weeks, within one grading period; but particularly at the first grade level, the entire year covers teaching only a relatively few skills (as the skills are fairly high level at that grade) and so a student in the first trimester or quarter might be expected only to reach part of the standard.
For example, if your student were in California, the California Core Standards for Mathematics include the following:
Represent and solve problems involving addition and subtraction.
- Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
- Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
This concept is likely introduced in the first trimester, and some students might start out proficient in it - students with academically focused preschools, for example, likely will. But most students will not know how to add going into first grade, and so will spend much of the year working on this skill. It will be introduced perhaps in the first trimester, and then, depending on the curriculum used, it might be practiced for the entire year - for example, with Eureka (the curriculum used at my local school), they have "sprints", which are long lists of short, related problems (think, "5+4", "5+9", "5+2", etc., all ten 5+ facts repeated about 30 total on a page), that both serve as a way for the teacher to gauge how a student can add, and reinforce the addition facts.
In order to show parents how their students are doing on these skills, report cards will generally show a student is either "proficient" in a skill (meaning they have mastered that skill), "nearly proficient/approaching proficiency" (meaning the student is not yet proficient at the skill, but has mastered some elements), "minimally proficient" (does not yet have significant mastery of the skill), or usually something that indicates the student shows no evidence of proficiency (wording varies a lot on that level). (Some schools also have a higher rating than Proficient, but as that's not really a standard, it's less easy to define.)
It is hard to tell whether a "nearly proficient" is a good score or not, particularly in first grade. However, for the most part, in February it is not unexpected for many of the skills to be "nearly proficient" rather than "proficient". My children both receive "nearly proficient" marks on most of their pre-may report cards in various skills, and even some "minimally proficient", but both typically progress to "proficient" in all skills by the final trimester. The best thing to do is to use this report card in the teacher conversations - hopefully you have a meeting with the teacher about as often as report cards come out, most schools do this by design - and have the teacher point out which skills you can work on. Nearly all skills will continue to be developed over the year in the first grade, but this is really important for the teacher to explain as it will depend on the skill, the teacher, and the curriculum.
Your school should have a "report card explainer" that will go in more detail about what the specific meanings are for the specific standard terminology, such as this one; it may not match that specifically (this was just randomly picked from a search, but there are many - pick the one for your school district). This usually is sent out with report cards. If this was't sent out, ask!
If you want to learn more about the standards, you can read the standards for your state (these are mostly state level). For example, for California the math standards are here and the "English" (meaning reading/writing for the most part) standards are here. Each state's standards will be a bit different; however, they will likely be based in part on the Common Core standards. There are some good "explainers" that can help you understand what kinds of things your student may be expected to learn as part of these skills; for example, these parent roadmaps are grade specific explanations of what is being taught and include example problems.
