It doesn't have an equivalent in English. I know that in Japanese, it's the same with -te form. I don't know about Swedish.
It's basically used when a chain of verbs will be done one after another. The point here is, the emphasize is not on the verbs themselves. Generally verbs in 'ip' form are not in the center of attention. They just need to be done, that's all. The focus is either on the last verb, or on that the chain of verbs being done together, consecutively. This form is generally used when you tell somebody what (actions) you did or will do in a story telling fashion, or when something needs to be done before doing something else.
Verbs that take -(y)ip suffix are always used in stem (imperative) form, but in meaning they have the tense of the last verb. 'ip' form can generally be replaced with the form of the last verb when it's used in past or present tenses, but not when it's in continuous or future tenses. Like:
Çarşıya gidip geldim -> Çarşıya gittim geldim (This is okay)
Çarşıya gidip gelmiş -> Çarşıya gitmiş gelmiş (This is okay)
Çarşıya gidip gelirim -> Çarşıya gider gelirim (This is okay)
Çarşıya gidip geliyorum -> Çarşıya gidiyor geliyorum (This is not okay, don't use this)
Çarşıya gidip geleceğim -> Çarşıya gidecek geleceğim (This is not okay, don't use this)
Verbs in 'ip' form are considered as adverbs in Turkish grammar since they answer 'how' question.
I hope I didn't miss any point to cover.