With social networking services (SNS) such as Facebook, Twitter, and Instagram, you can connect with people all around the world.
"You can connect with people all around the world with social networking services."
Prepositions connect clauses together into complex sentences. A complex sentence is one which has a principal clause and one or more subordinate clauses. Subordinate clauses are also known as dependent clauses.
The first clause is "You can connect with people all around the world". This is the principal clause. It can stand on its own as a sentence, independently of the other clause.
The second clause is "social networking services (SNS) such as Facebook, Twitter, and Instagram" This is a subordinate clause. It is only useful as a fragment of a longer sentence. It expands upon the information in the principal clause.
To connect a subordinate clause into a sentence, you need to connect it to the principal clause. The grammatical tool for bolting a subordinate clause to a principal clause is called a preposition.
The more usual placement of a subordinate clause is after the principal clause. In these cases, the preposition sits at the beginning of the subordinate clause, and as a result the preposition naturally sits between the two clauses.
In this example, the statement has the sentence of the form subordinate clause [followed by] principal clause. The preposition still sits at the start of the subordinate clause, even though it is still acting as the connection between the two clauses. This is because it is, in a sense, telling how the subordinate clause relates to the principal clause.
It means, by having/using those services, you can achieve your connection with people around the world. Think of the negative:
Without SNS you would not be able to connect with people (as easily)
You could easily substitute using or through in the sentence. Some languages show this relationship explicitly, for example Japanese uses de to mean by way of.