I see this occasionally.
Opening my router confirms I'm connected to the internet. The problem is therefore the fault of the ISP. Your ISP's signal has a base carrier wave to which data is added. In "old timey" radio you did that by amplifying either the wave's Amplitude (AM) or the Frequency (FM).
I say that to say this, you can have the signal carrier but no data. That allows you to be connected to the internet but no data is being sent by your ISP. No data = no surfing, email and so forth.
Given time, your ISP will realize the situation and fix the problem; usually it's quite temporary. If it keeps happening, you need to complain to the ISP.