I always think of reduplication as making something "fuzzier". So you know how it can be used to pluralise things - I think of it being the difference between "That dog" and "The general collection of dogs, not any particular one"
So with bermain-main, you're not playing a particular game, you're running around from fun thing to fun thing.
berjalan-jalan - you're not walking to a particular place, you're just walking wherever the mood takes you.
berjaga-jaga, you're not guarding against a specific threat, you're keeping your eyes open, looking here and there for whatever might happen.
I once compared it to the difference between thinking of a single electron vs. an "electron-cloud" if you know anything about particle physics.
According to my grammar book, an intransitive reduplicated verb can have the following five meanings :
Makna verba taktransitif perulangan ada bermacam-macam:
1) Perbuatan yang dilakukan tanpa tujuan khusus.
2) Secara berulang atau terus-menerus dengan variasi.
3) Resiprokal (kesalingan).
4) Ada intensitas yang tinggi sehingga hasil perbuatan yang superlatif.
1) Action that is being performed without a specific goal.
2) Over-and-over again, repetitive, with variation.
4) High intensity so that the outcome is superlative.
Source : Tata Bahasa Baku Bahasa Indonesia (Edisi Ketiga).
Reduplication (whether of nouns or verbs) is one of my favourite Austronesian grammatical features. It's so intuitive, so it seems like it's going to be easy to figure out the range of its meanings, but then it surprises you with the sheer amount of nuance that can be expressed through it.