on this side / this world
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on this side
Indicates a position on this side of something, as opposed to 'jenseits' (on the other side / beyond). It is often used with the genitive or with 'von' (of/from).
Diesseits des Flusses ist das Ufer flacher.
On this side of the river, the bank is flatter.
The word is made up of 'dies-' (this/these) and the ending '-seits', which refers to a side. So it literally means 'on this side'.
Diesseits der Mauer ist das Betreten verboten.
On this side of the wall, entry is forbidden.
When 'diesseits' (on this side) is used like a preposition, the following noun is usually in the genitive. In spoken language, the simpler construction with 'von' + dative is also often used.
Diesseits des Gebirges herrscht ein anderes Klima.
On this side of the mountains, a different climate prevails.
In philosophical or religious texts, 'diesseits' (this world) is often nominalized ('das Diesseits') and refers to earthly life. You can recognize this meaning from the context of life, death, and spirituality.
Er glaubte, man solle das Diesseits genießen und sich nicht nur auf ein Leben nach dem Tod vorbereiten.
He believed that one should enjoy this world and not only prepare for life after death.
over there
'drüben' and 'diesseits' both describe a side in relation to a boundary, for example a river, a street, or a border. But they point in opposite directions. 'drüben' means the other side, that is, the side over there. 'diesseits' means this side, that is, the side here. You can confuse them because both talk about sides. 'drüben' is very natural in everyday language. 'diesseits' sounds more formal and often appears with a genitive or with 'von', for example 'diesseits des Flusses' (on this side of the river) or 'diesseits von Berlin' (on this side of Berlin).
Diesseits des Flusses gibt es nur wenige Häuser.
On this side of the river, there are only a few houses.
Das Kind wartet drüben vor dem kleinen Laden.
The child is waiting over there in front of the small shop.