it's tough to explain a quote without knowing the context, but if I understand the concept, here's my interpretation. For the first part, we're not called to be comfortable. Everything is not cozy and easy and simple. If it is, then there's something wrong ("In the world you will have trouble..."). We shouldn't be seeking out a situation where everything is calm, cool, and collective, because ultimately we're living in a world of chaos, and if we're comfortable in this setting, there is something wrong.
For the second part, I think it's talking along the lines of having a faith so strong in God and willing to step out beyond what you feel comfortable doing (because of a calling by God), that you're not depending on yourself or others or anything other than God. We should be completely and utterly dependent on God and no one and nothing else. Not our own abilities, not other people's help, not anything.

Again, I think it's pretty dangerous to interpret statements out of context, but hopefully that gives some insight in it.