"BU" is an acronym for 'brilliant uncirculated.'
1903 is the year the coin was minted (made)
It could mean anything depending on the coin. What country? What year? What denomination? What does the coin appear to be made from?
Numbers on a coin usually signify the year it was minted.
If you mean the first coin made by the first US Mint it was the 1793 Half Cents issued in July of that year.
If you mean one of the brass coins currently circulating, they are worth only face value. If you are talking about a commemorative coin, please include the year of the coin and if it is a proof or uncirculated coin.
A date set is one coin from each year that type of coin was made using the most common highest mintage lower value coins.
If no year is listed, use n.d. which stands for no date.
A year mark is an inscription on a coin denoting the year in which the coin was produced or issued.
Just the year does not make a coin rare.
What does it say on it? Most modern bullion coins will give the weight of the gold in the coin in troy ounces on the coin somewhere. If your coin has that, it is rather easy to find your coin's value, just simply find the value of gold in troy ounces that day and figure out how much your coin is worth from that. If your coin doesn't have a weight listed, it should have identifiable characteristics such as the year, design, country of origin, and other ways to identify your coin. Without knowing the details about your coin it is impossible to truly answer your question.
It depends on the coin and the year where it comes from.
Please post a new question clarifying what you mean by "late 1860". Do you mean "late in the year 1860", or a coin from the latter part of that decade? If you mean a coin from the end of the decade post its specific date because that's very important.