Adjective: local (of a nearby location), native. Noun: (colloquial) local (as in nearest pub).
In our example, paikallinen appears in its illative singular form, paikalliseen, and is used as a noun. In illative case it has a meaning like ”into a local” or if we guess that OP (a Finnish cooperative bank with many local and regional branches) is making a bit of a play on words here, ”into your local (pub)” when referring to its local branches.
Paikallinen comes from paikka, meaning ”place,” ”area” or ”region” plus the suffix -llinen, used to form adjectives indicating likeness from nouns.
Let’s break down the whole phrase, ”Astu sisään paikalliseen.”
Astu is the second person imperative form of astua, which means ”step on,” ”tread on,” ”pace,” or ”stride.” (See astua conjugated here.)
Sisään is an adverb that means ”into,” ”in” or ”inside.”
Our phrase perhaps best translates as ”Step inside your local.”