Why does Blacks Law Dictionary say the POTUS is the highest magistrate in the land?

Years ago, I was looking at a Black’s Law Dictionary and was surprised to read that the President is regarded as the highest magistrate. What exactly is a magistrate, if not a judge?

And in a similar vein, one used to hear of ‘police courts’ for minor offenses. Do these still exist? Wouldn’t there an implicit conflict of interest? How did/do police courts work?

To address your second question, the original Police Courts were British.

" However, in 1839 the City of London formed a separate but similar police and in the same year the various police offices, including Bow Street ceased to exist. The various police offices were converted to police courts–the magistrates no longer having any policing role and the constables offered the opportunity to join the Metropolitan Police Force. "

In other words the name arose because of the magistracy’s original connection with the police. The term survived in the UK until the 1960s when it was changed to Magistrate’s Courts. (A magistrate in the UK is a person of good repute in the community who presides over minor cases. He has no legal training and is advised on matters of law by a Clerk of the Court, who is a lawyer. All cases will first be heard by a magistrate, who refers serious offences to committal by trial of judge and jury.)

Perhaps the US police courts began under similar circumstances?

Extract above taken from Rutgers.edu

I’m inclined to think that ‘magistrate’ is, in this [obsolete] sense, one who administers the country in accordance with the laws. The Consuls in classical Rome ran the republic, but they were judges too and did sometimes try cases.
Actually many magistrates in England these days are permanent paid positions and lay magistrates are becoming rarer.

Rarer?

This is from the
Magistrates’ Court Committee

“Apart from the lay magistrates’ of whom there are about 30,000, there are also 95 District Judges (Magistrates’ Courts) (formerly Stipendiary magistrates). These are paid professional lawyers who sit alone in courts where there is a high volume of work such as in London and in larger cities. However, many commission areas now have a full time District Judges (Magistrates’ Courts) who will sit in more than one location. District Judges (Magistrates’ Courts) can also be called in by a local bench, e.g. at times of abnormal pressure. Stipendiary magistrates have all the powers of a lay bench, i.e. they can decide guilt or innocence and pass sentence on their own.”

As has already been said, “magistrate” (Latin magistratus) was anyone who had been elected to one of the highest offices of the Roman Republic, namely consuls, praetors, quaestors, censors, and aedils. Since Rome did not have a balance of powers in the modern sense, many of these exercised executive as well as judicial powers. The word has later been used to signify a variety of political offices; in some countries, especially the local administration of a town/city as a whole was (and is) referred to as the magistrate. I guess the -. nowadays more common - meaning of magistrate as a judge sitting over minor crimes derived from this context of local administration.

Would it be too obvious to suggest that the answer to the OP can be found by seeing how Black’s Law Dictionary itself defines ‘Magistrate’?

Which is ‘A public civil officer, possessing such power - legislative, executive, or judicial - as the government appointing him may ordain. In a narrower sense, an inferior judicial officer, such as a justice of the peace.’ It then go on to discuss U.S. Federal Magistrates.

Originally it was used in English only in the more general sense, but over the centuries has come to be applied, both in the UK and the USA, to the various specific offices already mentioned as an actual job title.