I have often seen how many people say that mortality rate is very low in modern times than in the past, that people die because of illness much less today than in other times in the past. I have also seen graphs of world populations from as early as 10,000 BC. How do historians know these information?
There are a variety of ways. Generally they break down into records and archeological data.
It should be noted that records before around 1500 are VERY spotty, and thus any estimates before then tends to be very unreliable, and we don't get anywhere close to "complete" records until maybe the 1700's or so. (and even then there are often gaps, due to fires, war, etc. destroying records) and that's for places where we have good records.
The most reliable records tend to be those that governments do to keep track of their population, they record births, deaths, etc and thus you can look directly at the records and figure out things like mortality rates. There are several possible issues with those, for one thing, they only record what well... is recorded, so if the government for one reason or another fails to record a birth, it won't show up in the statistics (this can be especially important for mariginal groups, or in situations where the recordkeeping can't be done because of eg. war, plague or similar) the second, which is an issue for many of the earlier records is that rather than recording births and deaths they record baptisms and funerals (since these records were kept by the church) this means that if a child died before baptism it would often not be recorded. In some cases we are lucky enough that people record case of death, as well as other information too! There are also other forms of records that can sometimes be used (like censuses or tax records, that sometimes notes age)
For areas where we don't have these kinds of records, it gets much harder. Sometimes we can use eg. human remains to estimate ages and causes of death, but that by neccessity means we're dealing with a small sample size. For population as a whole you there are various methods of estimating how many people can live in a particular area based on how much land was under cultivation, how many houses in a city, etc. But these are by their very nature not particularly exact. (whether or not you estimated people lived 4 or 5 people in a house would have a huge impact) and also often relies on extrapolation from areas with better data.