The German version of Wikipedia elaborates on this:
Der Bundespräsident ernennt die vom Bundeskanzler Vorgeschlagenen zu Bundesministern und Staatssekretären. Inwieweit der Bundespräsident dabei personelle Auswahlkompetenzen besitzt, ist im Grundgesetz nicht geregelt. In der traditionell gelebten Verfassungsrealität hat der Bundespräsident ein formales Prüfungsrecht, also bspw. bezüglich der Frage, ob der Vorgeschlagene den formalen Anforderungen des Amtes entspricht (bspw. ob er Deutscher ist, das Mindestalter erfüllt etc.). Ein weitergehendes materielles oder personelles Prüfungsrecht ist zwar im Grundgesetz keineswegs ausgeschlossen, hat sich aber in der Verfassungswirklichkeit nicht entwickelt. Die heutige Tradition, dass sich der Bundespräsident in die Personalpolitik des Bundeskanzlers nicht einmischt, geht zurück auf ein diesbezügliches Ansinnen von Theodor Heuss, der sich vor der Ernennung der Minister des ersten Kabinetts Adenauer eine Ministerliste vorlegen lassen wollte. Adenauer wies diese Forderung jedoch zurück, Theodor Heuss gab nach und etablierte so die seither geübte Vorgehensweise, die auch bei der Entlassung eines Ministers oder Kabinetts angewendet wird.
A minor detail is that the president is supposed to check whether the candidates meet formal requirements like being a German citizen or meeting age requirements.
More importantly, none of this is clearly defined in the constitution but stems from a tradition established around the time the current constitution was enacted. The framers of the constitution might have intended for the president to have a more active role and there is nothing formally preventing it.
In fact, in 1949, Theodor Heuss asked Konrad Adenauer to provide a list of candidates from which he would choose the ministers himself but ultimately had to cave in and name the people Adenauer wanted. But the president could still, in principle, refuse to name someone and the chancellor would typically seek informal contact beforehand to avoid that. Case in point, in 1953, Heuss forced Adenauer not to (re)nominate Thomas Dehler as justice minister and this time, it's Adenauer who caved in.
This shows that avoiding open conflict and, to this date, always following the advice of the chancellor does not mean the president has absolutely no influence in the process. At the same time, breaking with tradition is not risk-free and that means such a prerogative can only be used in really serious cases.
Generally speaking, it's not uncommon for the details of a constitutional framework to be elaborated over time and to differ sometimes markedly from what the letter of the constitution seem to suggest (the role of the president in the third French Republic is another example). But going back to amend the text is just a lot of trouble and typically not considered necessary.
Beyond that, it means two people are involved. I have no idea whether that was the original intent but it might provide some sort of safety mechanism in times of crisis (say a minister is about to take some important decision, the chancellor cannot just prevent that from happening by dismissing the minister, he or she must wait for the president to formally act on the recommendation for it to be legally effective).