
sich vermehren
to reproduce
The number of living beings (people, animals, plants) increases through reproduction.
Kaninchen vermehren sich sehr schnell.
Rabbits reproduce very quickly.
to reproduce / increase
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to reproduce
The number of living beings (people, animals, plants) increases through reproduction.
Kaninchen vermehren sich sehr schnell.
Rabbits reproduce very quickly.

to increase
To increase the amount or value of something.
Er hat sein Vermögen durch kluge Investitionen vermehrt.
He increased his fortune through smart investments.
The word 'vermehren' (to reproduce / increase) is inseparable and is derived from the word 'mehr' (more). The prefix 'ver-' here strengthens the idea of increase that is already contained in the root 'mehr'.
Durch die neuen Maßnahmen soll die Sicherheit vermehrt werden.
The new measures are intended to increase safety.
The use of 'vermehren' (to reproduce / increase) changes the meaning. 'Sich vermehren' (reflexive; to reproduce) is used for living beings that reproduce. 'Etwas vermehren' (transitive with an accusative object; to increase something) means to increase an amount or a value.
Die Algen im Teich haben sich stark vermehrt.
The algae in the pond have reproduced rapidly.
The reflexive form 'sich vermehren' (to reproduce) is used almost exclusively in biological contexts for animals, plants, bacteria, or cells. Typical adverbs are 'schnell' (quickly), 'rasant' (rapidly), or 'unkontrolliert' (uncontrollably).
In diesem feuchten Klima vermehren sich die Mücken rasant.
In this humid climate, mosquitoes reproduce rapidly.
The transitive form 'etwas vermehren' (to increase something) is often used for abstract things or possessions. Typical objects are 'das Vermögen' (fortune), 'das Kapital' (capital), 'das Wissen' (knowledge), or 'den Reichtum' (wealth).
Durch Lesen kann man sein Wissen täglich vermehren.
By reading, you can increase your knowledge every day.